Proven with what? Our grasp of physics can only let us understand what probably happened minutes after the Big Bang occured. According to this model, complete removal of information occurs at the end of the cycle, or aeon, when black holes evaporate and the universe returns into a pristine state, just like a blank slate.
I think it's easier to understand what we are talking about if you imagine the universe as a white blanket.
Before the big bang occurs, the blanket perfectly smooth, just like it was well ironed. Then, a massive jolt causes it to fold, crease and wrinkle: this is information, i.e. matter. Entropy could probably act as a gradual, unstoppable force that gradually puts the blanket under tension again.
The end of universe, therefore, is the return to a pristine state completely devoid of information. Suppose you spill a cup of coffee over the blanked: it is now tainted, but this doesn't necessary interfere with the distension process of prohibit the blanket from returning to a perfectly smooth state. However, if you take a look at the tainted blanket, it obviously isn't perfectly white as before.
Therefore, the Big Bang acts as a creator of new information, not as a destructor of previous information.