Is it possible to theoretically keep the Avatar timer from fully filling indefinitely if you’re careful, or does the timer advance slightly faster than opportunities to take it down appear, and eventually it becomes impossible to overcome?
It would be nice once the final assault is unlocked to be able to dick around and enjoy being OP for a bit before ending the game. I don’t want to risk losing the game though.
Will there always be sufficient opportunities to bring the Avatar time down, or will you eventually lose no matter what?
In the base game without mods, I find that eventually you run out of facilities to take out, which is the only way to reduce the timer. Nothing prevents you from unlocking the final mission and performing it as late as possible. You probably run out of patience and things to do before you are forced to do the final mission.
In XCOM2: War of the Chosen you can get special covert operations with each of the three factions to reduce the timer. If you prioritise them, you have a decent chance to delay the inevitable forever.
With mods, you can simply disable the timer if you do not like it.
Also, keep in mind that when you run out of time (that is, the doom bar fills up completely), you still have some time to trigger the final mission. You are never really in danger of not being able to win, other than not being prepared, or by the doom timer filling up before you are ready to play the final mission.