Yeah check out my post in the Playthroughs forum called Fastest Game Over Ever if you want to see one in which the base got attacked on day 2 after shooting down a small scout. It can happen, fortunately a fast game over doesn't take a lot of play time away from you--but you can also save after you get your starting changes done, then if you lose quick, try reloading and see if it doesn't happen that way the second time. Just make sure you have save scumming allowed in the options, or if not do something different when you reload. Usually one of two things happens:
1.) it was already decided when you saved, and it happens basically the same way (same ship arrives in the same region at the same time, etc.) - just give up and start a new game or skip the mission if you can
2.) it wasn't decided and the game plays out differently, probably easier - if you lose quickly in a very different fashion, it's a fluke and you can probably just try again and do fine
I have completed the vanilla game on PC and PS1, and distinctly remember that especially on beginner level, it introduces aliens and ships slowly; first you get small UFOs, then mediums, and so on. The first aliens you encounter are usually sectoids, and the game builds up to reveal the stronger enemies.
I missed this earlier. The game actually goes a little strong on you right from the start. You tend to encounter sectoids and floaters in the first month and they are a godsend in small ships, but sectoids are very dangerous in larger ships and cyberdiscs remain the most effective hovertank busters into the late game. You're going to get a terror mission some time in the first month and from then on you'll tend to see more large ships than mediums. The game doesn't really go easy on you unless you can get personal armor while the aliens are still using plasma pistols, power suits while they are still using plasma rifles, and blaster launchers/psionics by the time they start cheesing you with ethereals. So I personally find the difficulty is a matter of research choice--sometimes I deliberately skip laser research in favor of making a beeline to armor research, and just try to squeeze in plasma guns before snakemen come along.
You can also buy time by scoring just enough points to stay afloat, so the aliens don't grow as fast. Sometimes beginners feel like the game is easier because they aren't shooting everything down and instead just go to landed craft and terror sites, which reduces retaliation missions and alien power creep. Brilliant, I think. I go crazy shooting down everything and it makes the game harder, which is great because I'm pretty used to it--but as many ships as I get coming at me wouldn't be good for a new player.