How is enemy progression determined in Xenonauts?

Solution 1:

This is almost certainly triggered by the reaching the objectives the game sets for you. They are shown on the map in the lower right corner.

In my current playthrough I waited a long time to research "Alien Interrogation", which was suggested as my goal after capturing an Caesan alive.

I played several missions before that and they all were equal in difficulty, featuring the same UFOs and the same aliens with the same equipment. Neither time nor other research nor the second base I set up in the meantime changed anything about that.

After researching "Alien Interrogation", I instantly faced new enemies with new equipment and a new UFO type.

So while I cannot be absolutely sure that the game won't progress after an unknown period of time which I simply have not hit yet, I am pretty sure you should be safe from enemy progress as long as you don't do what your mission requests.