If it actually existed, then obviously I would subscribe to whatever theory most accurately described how it worked. That's science.
If you're asking which theory I would predict is most likely, knowing only that time travel was possible as a starting point, then there are only two that I'm aware of that are logically consistent. Either:
Single fixed timeline, whereby if you go back in time then whatever you do there was already a part of history from the start. You won't be able to "change" anything because you were always there. This is the approach described by the Novikov self-consistency principle.
Multiple worlds, in which if you go back in time you just end up following a different "branch" of history forward from there.
Any of the models that let you "change your own history" are logically inconsistent and therefore utterly impossible. They just can't exist, like a square triangle or 1=2. They may be fine for entertaining movie plots but don't take them seriously.
I just imagine if life is a simulation and everytime someone travel back a new branch created but then coming back to present timeline you have to fix all the merge conflicts.
Slightly more seriously (but only slightly), what if what we see as Heisenberg uncertainty and probabilistic wave/particle weirdness is actually the result of multiple overlaid timelines caused explicitly by time travel, and if time travel wasn't possible, the universe wouldn't have those properties?