I think there is an alien research mission which is "hardruled" to spawn in the first month, using the first alien race defined, and spawning in the region where the xcom base is, to ensure that a player has something to play against in the first month.
In vanilla, this gives you a sectoid research in your first base 100% of the time. Since it is defined somehow with rulesets and not hardcoded, it can be changed, but not quite in the way you are implying.
As for your terror mission idea, I think it is possible to make a mission which ends as a victory after a set number of turns (provided you survive). This could sort of work: The team is deployed in the hot zone and has to make a difference before the national guard comes in. If you make the bonus for winning very small, the end result can be 100% based on how the player does:
- Kill a lot of aliens/save a lot of civilians = lots of points.
- Don't kill much/lose lots of soldiers or civilians = lose points.
You could just hide and do nothing (so not meeting your 75% alien kills), but then you won't be getting points for aliens killed and presumably they will kill the civilians, so you would lose points overall for not doing well. It changes the focus, but it could be interesting.
Maybe you can use that as a "common mission", so it doesn't become the potentially annoying after a while "hunt the last alien", and keep typical terror where you have to finish things off yourself as well, on a monthly basis (maybe then the national guard can't show up within a day, or it's in a large city and it has to be dealt with in less time than a coordinated assault takes to organize, so it's you or nothing.)