Not saying that I can 'prove this but as something to enquire into maybe? A hypothesis
What if the Big Bang happened within what could be called 'awareness.' Being within this awareness, everything that was 'born' of this Big Bang is also actually made from the essence of awareness. So we might then have awareness that is still is in its state 'before' the Big Bang (maybe call this the Unmanifested) yet also also this awareness in forms as made 'after' the Big Bang (maybe call this the manifested).
Now in this model, would it be possible to question whether the intellectual mind could possibly be that which contains all of awareness or is it more likely that the intellectual mind is like a filter for this awareness, that divides things into a 'this' versus 'that' s (some might call this polarity) so as to try and understand?
In this way, could the intellect ever really understand the whole of awareness given that its nature might be to divide awareness into this and that? I'm not so sure...Maybe something closer to understanding would involve letting go of the intellect and beginning to feel/tune into* the awareness 'before the intellect (call this the intuitive if you want) then this can join and play with the logic of mind - this joining that might then be called the truly rational mind.
A final question might be : Is it possible that the intellect that needs proof of awareness might eventually be found to be that which gets in the way of knowing awareness - that as one lets go of the need to prove awareness, then awareness will reveal itself to, and through, us in our own unique way?
And this is only one way of looking at these questions. Not THE way and certainly not 'if you don't agree with what I wrote then you will surely go to hell' way. either Just a way, is all. Maybe not the 'best' one. Or even particularly one I might choose to use often...
*Some might say 'tuning into' is what prayer is really for but who knows?