It doesn't "prove" the existence of time. Time is a convention of perception, an agreed-upon illusion. It stems from the belief that objects persist.

There is no objective way to prove the existence of time as it is a construct that is primordial to the material universe, which would fall apart without it keeping moments neatly organized as an apparent sequence. From within the universe, it seems inherent. THe two things that might disprove it are some quantum phenomena that appear to transmit information in zero time, and spiritual phenomena in which individuals transcends time and discover the creative center of things as their own time-free origin point. Rare, and beautiful when it occurs.

A