Meh, Singularity is overstimated. Singularity ignores the fact it is impossible to simply iterate on a technology. Technologies can become mature, or stop advancement because the next step requires a material discovery, or even a paradigm change.
A good example: Guns. Guns in 1900 are all semi-auto, bolt-action stuff, with semi-automatics being relatively recent. By 1950, we had assault rifles like the AK47 and the FN-FAL. 2020 guns are pretty much 1950 guns with lighter materials and extra stuff like picatinny rail, etc.
This is because firearms became a mature technology after WWII.
Computers are also a good example. Computers as we know them came about in the 80s. I am not old, but I lived the nineties and the 2000s. You could buy a top computer, and next year, it would be obsolete junk upstaged by the newest shiny stuff. It was ridiculous.
That stopped in the 2010s or thereabouts. A 2010 and a 2020 computer are pretty much the same thing, but the 2020 computer just has ten extra years of tech. A top of line 2010puter would pass muster today. By comparison, a 1990 top computer would be a museum piece in 2000, and the 2000 topcomputer would likewise be junk in 2010.
I think the biggest impediment to AI is the current computer architecture. Look at the human brain. Faster, better, stores more info than hundreds of hard drives, does actual thought and emotion, small, and barely uses enough power to switch on a fridge light. No computer does this and occupies the same space and has the same use of energy.
We cannot beat the human brain with what we call a computer nowadays. We need a paradigm change here. A quantum leap. Maybe quantum computing is the key.
True AI in 2050? More likely, 2500.
There's the chance the aliens are far older, through. But someone in this forum once pointed out that, if you assume life evolved naturally, and their planet followed a similar time-table to ours, then the time for life to appear in the universe is... Right about now.
This is because you need stars of enough metalicity (AKA materials that are not hydrogen and helium) to get a star long-lived and hot enough, and solid planets with enough minerals and such to sustain life. Then enough time for life to evolve properly.
Then there's the fact alien minds are, well... Alien. We don't know how they think. Alien Intelligences are an enigma.
And there's always the issue of tech. Renassaince Europeans were two millenia ahead of the Amerindians, whose technological level was somewhere between the neolithic and the early bronze age. They pretty much won by accident, because of diseases. Europeans still died to spear stabs and arrows anyway.
If America had large, centralized polities at the level of say, the Assyrian Empire, then it is likely things would have turned differently. Hell, Pizarro pretty much lucked out in beating the Incas, the closest thing. Had they been at full power, Pizarro would have been flattened and so would anyone else before 1650.
X-COM is actually logical: The aliens don't attack directly, because taking worlds is hard. Worlds are immense, full of people. If you want to win without bombing everything, you need hundreds of millions of soldiers, even if the locals folded like a cheap lawn chair, because otherwise they might as well create guerilla cells outside your control zones and local polities might start double-dealing. Far easier to coopt the local leaders, especially if you control minds and can play the long game.