I don’t think time travel is impossible because of paradoxes. I think it’s impossible because time is not a place you can go to like you can go to Jersey.

Time is a word that describes the way the universe evolves from one arrangement of matter and energy to another. “Time travel” is just rearranging the universe into an arrangement that obtained previously. But it’s impossible to truly visit the past this way, for two reasons.

1. Putting the universe back into a previous state would require more information and more energy than could possibly be gathered and deployed even when the state is one that occurred relatively recently (remember light travels at 300,000 km/sec, so you’re looking at getting all the data about every particle within a sphere of that radius just to go back one second, and somehow finding the energy to push all those particles back where they were; not happening)
2. Even if you could, the second law of thermodynamics still holds, so while you may be reversing entropy within the sphere where you’re doing this rearranging, outside the sphere the amount of heat being dissipated has to more than make up for it, which means your rearrangement of the past is just a copy, existing in a universe that is itself still evolving forward in time.