Tape recordings can sort of prove that there is a past. But it is a past that most people consider dead and gone. To actually prove that there is such a thing as a past, scientists would have to somehow devise a way to reach back into time, perhaps at the quantum level, and yank out a souvenir that somehow wouldn't affect the past enough to change history, or cause a time travel paradox. Such a physical souvenir would be, for all practical intents and purposes, proof that there actually is a past. I believe something like this will happen in my lifetime. I Don't really believe that people going back to the past in order to change history is possible, however.