This is a slightly off-topic article that relates to my introspecion on the origin of the alien intelligence(s) that have visited Earth. First, I begin with explaining just how rapidly we showed up, and how the universe may yet blossom full of life but it may simply be too young to be covered with interstellar civilizations.
The Fermi Paradox states that our own galaxy has got to have millions of life-supporting planets around stars some of which are older than our sun, and some of those planets would likely produce alien civilizations which could traverse the Milky Way in millions of years even without faster-than-light travel. The paradox is that despite all the time that has passed (the universe is ~13.8 billion years old), we see no evidence of extraterrestrial intelligence.
I think 14 billion years is a bit early to start saying there's nobody out there.
Let's start with a list of the things a life-supporting planet needs to produce a civilization--and I'm going to use a modern and loose-fitting set of needs which may differ from the necessary things you've heard about:
1.) nutrients for biochemistry - the planet's surface must be rich in substances that can create biochemical molecules. This probably means hydrogen, carbon, nitrogen, and oxygen and fortunately these are extremely abundant. They are also low density and so are likely to be found on the surface of the planet.
2.) an atmosphere to allow liquids and gases on the surface, many of which are important for biochemical interactions. Many planets form with an atmosphere but most lose it eventually.
3.) a stable environment that allows life to evolve for a long time without the planet becoming sterilized at any point.
You may have heard that planets have to be the exact right distance from their star, the 'Goldilocks Zone' if you will. That zone is actually a rather thick band, for instance in our solar system Venus, Earth, and Mars are all within this Goldilocks Zone. Venus and Mars are inhospitable because they don't have a strong magnetic field. Earth's magnetic field is constantly reinforced by the strong tidal forces between it and its large moon. Venus and Mars don't have a large moon. Once upon a time they both had flowing water on their surface and may both have had simple life.
The Downfall of Venus: This planet is Earth's twin, it's barely smaller and has about the same internal makeup, being made of mostly iron. It probably started off with a strong magnetic field and a moderately-thick atmosphere of primarily hydrogen. But over time its mantle cooled and began to stop moving, and its magnetic field waned. Its atmosphere bled into space and some event (seems to be connected to the loss of magnetic field) triggered intense volcanism which caused the surface to continually spew out tons of carbon-dioxide gas. Today the planet has a very thick atmosphere which is constantly being bled into space but is also being constantly renewed by the intense volcanism.
The Downfall of Mars: This planet is significantly smaller but still quite large enough to support life. Its internal makeup is low on iron, being much more carbon-rich and giving the planet a much lower gravitational pull than Earth. It probably had an atmosphere of primarily hydrogen initially, and it definitely had flowing water on its surface. We can see the evidence of this all over the surface: it is covered in lake beds, river chasms, deltas, oxbow lakes, and everything in between. But the mantle and core began to cool and it lost nearly all of its magnetic field. The low density composition of Mars and its lack of heavy radioisotopes likely made its core cool even faster, causing the magnetic field to wane more rapidly. It is possible Mars also went through a phase of intense volcanism--today we see giant volcanoes on its surface much like Venus has, but the ones on Mars are long dead and the atmosphere of carbon dioxide has grown very thin. The only thing keeping it from completely escaping into space is that some of the carbon dioxide keeps freezing onto the poles, and melting again. This delays its escape, but it's only a matter of time before Mars' surface is a vacuum. Eventually Venus will follow.
Why the Earth thrives: Earth has a strong magnetic field which holds in its atmosphere. This magnetic field is constantly replenished by internal motion and shear forces in the supersolid mantle. This mantle is technically solid and we can determine this by sending sound waves through it. The sound waves are blocked by the liquid core. The mantle is so hot that the rocky iron-rich material it's made of should be liquid or gas, but it's under so much pressure that it's solid. The pressure is so great, in fact, that these solids are deformed and pushed around almost like a liquid. The mantle ebbs and flows like a giant ocean of solid rock, creating tremendous frictional forces and magnetizing the planet as a whole. What keeps it hot is a twofold effort: the giant moon's tidal forces rip and tear the crust and mantle, generating heat near the surface, while the radioisotopes within the core decay gradually and produce heat from within. The mantle can't cool because it's being heated from both sides.
So how often can we expect to find a planet like Earth, with all those heavy metals and a large moon? The answer is less about rarity and more about time. When the universe first formed, it expanded rapidly but it took a very long time before it had cooled enough for matter to form. After about 150 million years, stars of pure hydrogen began to form, and we call these Population 3 stars. There were no heavy metals in these stars initially. Elements from helium to carbon can be produced in a small/main sequence star (like our sun) and after it fuses carbon in its core, it becomes unstable and sheds its outer layers in what we call a nova, trapping everything heavier than helium in its white dwarf core.
The metal gets outside of the stars by way of supernovae. These are caused by giant stars fusing all the way up to iron, which causes them to explode violently. The lithium through iron in the core still is trapped inside and the core becomes either a neutron star or a black hole, but the ejecta is released with such tremendous force that much of it is fused into the really heavy elements, and this is where most of the elements, such as gold or uranium are produced.
Most stars were stable for a long time, but some lived short lives and exploded young. Size was a big factor here, larger stars didn't last as long, but density was another factor. The lightweight population 3 stars burnt their fuel much slower than the majority of stars today, and so there was a long time before even population 2 stars became abundant. Population 3 stars would not have had any planets, but may have had other stars orbiting them.
It's hard to say when population 2 stars started to pop up, but gradually as stars exploded and new ones formed, some stars got heavier elements inside of them. These were the population 2 stars, containing heavier elements, but they were still very metal-poor compared to the population 1 stars that are abundant today. These population 2 stars may have had a few sparse bits of debris orbiting them, and they may have captured planets later, but overall they would be barren. They played an important role, however, as they would go through their life much faster and explode, enriching the universe with more metals so that eventually population 1 stars could form.
It was about a billion years after the Big Bang that galaxies began to form, and around the same time that the very last population 3 stars formed. Any population 3 stars (extremely metal poor) alive today are almost certainly over 13 billion years old, and many of them may stick around quite a bit longer as they very slowly burn through their fuel. By the time galaxies began to form, metals and heavier elements were spread all over the universe, albeit still in small amounts. Many population 2 stars formed, and gradually seeded the universe with more metals.
Around 4-5 billion years after the Big Bang, the first population 1 stars formed, rich (relatively speaking) with metals (astronomical term for all heavier elements) and these probably had planets around them. The first population 1 stars were as yet metal poor compared to what life needs, but early star systems could have had a variety of lifeless planets orbiting them. Maybe life started on a few of these, but it probably didn't get very far as those planets probably didn't have atmospheres, and the few that did would have lost them quickly without a magnetic field. This was around 10 billion years ago.
The oldest metal-rich population 1 stars formed around 7 billion years ago, 7 billion years after the Big Bang, when the universe was half the age it is now. These stars had rich accretion disks which would have given them an abundance of planets, some of which would be very large and have very thick layers of gases, compressed into deep oceans made of mostly hydrogen and helium. These are what we call gas giants or ice giants, depending on their exact composition. Don't let the name fool you, they're mostly liquid. Names in astrophysics tend to refer more to their composition relative to other objects, than it does to their specific traits.
Now we've finally got the first stars that can bear life-supporting planets, and it only took 7 billion years. From here, it's a matter of chance whether or not life gets off to a good start. It'll need a metal-rich planet--not necessarily as rich as Earth--I simply mean not a barren chunk of lithium. It's going to need to be rich in carbon, oxygen, and nitrogen, and it wouldn't hurt to have a heavier core to push all the lighter stuff up to the surface. It also needs a large moon and a protective gas giant. The gas giant provides that stable environment I mentioned earlier, ensuring that this rich accretion disk doesn't become a shooting gallery and prevent the planet from stabilizing before it's lost its chance to start life. But gas giants are abundant around these stars, so that doesn't eliminate too many. The biggest factor of chance here is getting that moon. They're rare because planets can't form with a moon like that--it would have been unstable during accretion and they would have merged. The only way for a planet to have a large moon is for it to gain the moon after accretion.
Earth seems to have obtained its moon when the Mars-sized planet Theia plunged sidelong into the Earth, merging the two and sending a large amount of material into a low orbit around the Earth. This likely happened about 4.5 billion years ago, perhaps only a hundred million years after the Earth formed and within the first billion years after our sun and solar system began to form. The material pushed into Earth's orbit would have coalesced into the moon we see today--built out of the same stuff as our planet, but barren because it lacks the heavy core. It became tidally locked with Earth and cooled, losing its magnetic field and atmosphere. Its core is probably completely solid. But it keeps us alive today.
Another possible way to obtain a large moon in a low orbit is for one to be captured into the planet's orbit. It would initially have a highly elliptical orbit, but close encounters with other bodies in the young star system would adjust its orbit until either it becomes stable, is ejected, or crashes into something. There may be other possible ways to obtain a large moon, but the vast majority of times it'll happen are in one of these two ways.
The chance of your protected planet in the Goldilocks Zone obtaining a large moon are slim. Most planets in the accretion disk never get struck by another planet, and the ones that do aren't likely to get a moon from it. If the planet hits too directly, they may shatter each other or just merge together, which one depending on the speed of the impact. If the planet hits a glancing blow, they may both keep on going, losing very little matter yet having their orbits readjusted. And if the planet does hit at a good angle, it may send the other planet reeling off on a bad orbit that might lead to it colliding with another planet or being ejected from the star system. The same poor chances exist for those rare planets that capture a large moon, for it has to become stabilized before it either gets ejected or collides with its new parent planet. It's like playing Russian Roulette every time you flip a coin until it lands on its edge.
But somewhere out there it's bound to happen. Still, that means it probably isn't very common in the early universe. But not very common 7 billion years ago would be far more common today, given how rich our galaxies are in population 1 stars. So that brings in the question: how long does life need to produce a space-colonizing civilization? Well let's walk through the Earth's development. It's 4.5 billion years ago, chance happened, Jupiter defends us, we got a large moon, and we've definitely got the materials for life to form. Now it's once again a waiting game.
The moon cools and the planet's surface cools. The moon was much closer to the surface than it is today, and it wasn't tidally locked. It created intense tidal forces, but the Earth's surface was able to cool enough for life to form. The hydrogen atmosphere acted as a weak shielding from the sun's ionizing cosmic rays, but life needed more shielding than that. The surface was probably a bit moist, but rocky, barren. No life formed yet.
Over the next hundred million years or so, the planet was bombarded repeatedly with smaller meteors and comets, and they may have enriched it with more water. One way or another, nearly all of the water it has today was probably on the planet within the first few hundred million years after it formed. Over time the impacts began to thin out, oceans formed, and within some of the warm, shallow waters complex molecules began to form. They probably came together quickly as soon as conditions were right. The oxygen and nitrogen would have readily combined with other materials to form many simple organic compounds. Carbon could form long chain molecules, allowing for many kinds of chemistry to happen. Water was the solvent and catalyst, mixing the reagents and driving them to form new compounds. And lightning provided ionization, splitting apart overly stable compounds and enabling special compounds to form which could not form in the absence of electrical ionization.
RNA and DNA formed in these oceans and it began to replicate itself, kicking off the process of evolution by gene mutation and natural selection. This all happened in the early years of the Earth, more than 4 billion years ago, and only maybe 1-2 hundred million years after Earth stabilized and became suitable for life. All life we have found on Earth is genetically related, suggesting that while life may have started multiple times on Earth and in multiple places, only one set ever survived to today. Some say it was the extremely lucky strain that didn't die to whatever killed the rest, but I don't believe that for a moment. I'll bet it gained a strong mutation and conquered all other life on the planet, rendering it extinct. During this time, meteor impacts may have sent life off the Earth and into space, where it is conceivable it may have survived and later impacted Mars or Venus. They, too, may have had life ejected into space where it landed on Earth. Maybe all life on Earth originated on Venus or Mars. Maybe the tough strains that survived space travel became the invasive species that killed off everything else. We don't know. But today Venus and Mars are hostile and we think probably lifeless while life on Earth thrives.
Eventually the DNA and RNA gained cellular bubbles which protected them while allowing genetic material and important nutrients to pass through the porous shell. These were the first cells and most of us say it was the first life, but I say life began at DNA creation. Where you draw the line is moot, however. But after this, single-celled prokaryotic bacteria (the first and most successful domain of life) thrived and began to fill the shallow parts of the Earth's oceans. They lived around 1-100 meters beneath the surface, deep enough to be protected from the sun but shallow enough to receive its warmth, shallow enough for ocean currents to churn up precious nutrients to sustain them. These first life consumed raw nutrients to sustain themselves and were not sufficiently developed to produce energy.