I have always been interested in theoretical physics.
However, I think it is by definition impossible to 'prove' reality.

Everything we experience is a result of sensory input. Think of it like in the Matrix movie. Conceptually, it is impossible to prove that we are not hooked up, matrix-style. The same holds true for the universe in general.

Look at the big bang theory: it says that everything came into being in a point without size. If there is a big crunch at the end and everything is compressed back into that point and annihilated, and there is no 'time' in which things can be measured (since time cannot mathematically exist before the big bang or after the crunch)... did we ever exist at all? do we then exist now? Or are we a dream without substance?

It's been mathematically proven that no system can be proven from within the axioms of that system.
Gödel's incompleteness theorems - Wikipedia, the free encyclopedia
Therefore I think it is impossible to use our brains to explain our very existence.

Even religion and science are not incompatible, since our understanding fails to accomodate for the things outside our worldview.
Fascinating debates, but you'll keep going for hours on end without any hope of proving anything.
This sort of thing is best discussed with a glass of whisky in front of a campfire.