Time travel could exist but we’d never know.

The human mind is constructed of atoms. Well, everything is made of them. Atoms are essentially immortal. To travel to any point in time is to travel to an arrangement of atoms. The ones that make up you were somewhere else, in another body or plant or dirt, 100 years ago. If you were to rewind time, you’d be removing the atoms from their current position, making up your body, and placing them in their original position. So, if you were to rewind time, everything would be as it were at the time, you wouldn’t exist, and nobody would know.

To by get around this, you’d either have to exclude your atoms from the reversal but, that causes problems for where they were so you haven’t gone back in time exactly. Or, you could figure out how to create atoms and create an exact replica of yourself and attempt to somehow prevent them from not existing when you rewind all the other atoms in the entirety of existence.