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We know that the velocity of an object impacts its impression of time (how time applies to it), that rate changing as we approach light speed. The same effect should apply at the ends of the universe, if expansion truly means everything is moving faster, and some particles can travel faster than light. But this applies to moving forwards through time at varying rates, not in traveling backwards in time.
I don't believe any proof establishes a way that a single particle, much less an entire body, could move backwards in time; existing proofs suggest we could move more slowly through time (like a pebble in a creek, maintaining its position as the water flows past it), but staying in-place and allowing time to catch up to you is not the same as actually moving backwards.
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