At one point for a small local convention, I ran a near-impromptu X-Com adventure. It had a nice setup with pregenerated characters.
I began with them all in an aerospace carrier, heading to the aliens' base on Cydonia. I described the long and horrible battles they'd each been through, and the cost of the alien war. They were armed head to toe with gear based on alien tech, and some of them were psychic, abilities boosted by alien technology. There was a pithy comment about what humanity had lost, and how much like their enemy they had become in order to survive. At this point, they hadn't even seen character sheets.
I then described how long it had been since their first mission, and then did a flashback, to where it was first contact... and handed out the newbie sheets, of them as a regular army unit who'd been dispatched to handle an alien crash landing in the earliest days of the encounter. We did that, then I laid some of the groundwork, and the survivors of that mission were given their updated character sheets when I faded to the "present" invasion of Cydonia. Those that didn't survive got new characters.
The invasion of Cydonia was pretty straightforward, with some interesting surprises, such as human collaborators in the form of groups like Majestic and even the CIA. Lots of fun.
I used a weird and obscure system for a game called Hidden Invasion, which, on paper worked well, but in play turned out to be very wonky.
It's one of those games I'd love to revisit sometime, perhaps with a newer rules system.