Is it possible to indefinitely keep up with the Avatar timer?

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.

The Avatar Project comes with two flavours of progress: facility progress and core progress. It all melds into the same bar, but the distinction is significant.

Facility progress is accrued individually by each facility as they are built and then periodically over time. Taking down one facility removes the progress accrued by this facility, and this facility alone, no more, no less. There is, as far as I know, no other way to remove that progress. The bright side is you can stay on top of it quite easily in the end game.

Core progress is accrued over time or with special events. Completing some objectives will remove some of that progress. Eventually you run out of objectives and the counter will tick inexorably till the end. There is nothing you can do against that in vanilla.

War of the Chosen offers Covert Actions and Resistance Orders to remove some of that progress. Resistance Orders will remove progress every month (but that requires unlocking said order, which could never happen as far as I know). Covert Actions are random, though you probably can get enough of them to significantly boost your game's length. There is however no guarantee you can keep that up forever.

If you want to keep your game alive indefinitely, you might consider cheating shamelessly using the RemoveFortressDoom command. Note that it will only remove core progress, never facility progress.