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It's complicated.
We have time at a large scale, and at a small scale. On the small scale, particles interact with time but in a mostly symmetric way, forwards and backwards are the same.
This would and does translate upwards, except it so happens in our "past" is a low entropy state, the "early" universe. Entropy tends to increase, energy spreads out, so what we call time, or more important causality, is the gradient of entropy.
For all we know, another universe could be in the past "before" "the big bang", which has its entropic time running the other way, also towards an expanding universe. (this is kinda adjacent to the big bounce theories, but does not postulate this repeats).
Now, there is a bunch of weird stuff general relativity permits with spacetime, including stuff that time travels (e.g. wormholes, warpdrives). This may or may not be possible to create if it doesn't currently exist, and it also may or may not be possible to use without getting destroyed even if it exists.
But interestingly, even if it were to be usable, be it wormholes, ftl warp stuff, or whatever, it may not break entropic time, only particle time which noone cares about. Causality may simply still be running forwards through that connection. That's still in the theorycrafting stage though.
There is yet more weirdness. For example, when you cross the event horizon of a black hole, you cannot go back, only slow your speed of going forwards, but you can with that travel through things that have fallen in before and after you. So compared to outside, entropic time is now in the direction of a spacial direction. Technically this lets you time travel through the particle-time axis, by some definition, but entropic time is still boringly pointing in one direction, though now by some more definitions that entropic time would causally sit after the end of our universe, so you have very efficiently entropically time-travelled to the end of the universe, infinitely far into the future.
So yeah tldr what we mean by time travel is not looking very possible lately (other than travelling to the future).