If no why can be thought of than the scientific theories are not complete, and the religions that answer this question will be more credible than science.
According to science the answer to why the universe exists is "Because it can". Because it can, it inevitably does.
You may not like that answer or consider it what you are looking for but in the absence of conscious intent what answer is there other than a technical answer of probability and inevitability?
If you are hoping to feed the very human need for actual conscious meaning or intent in your 'why' then you will need to turn to religion.
I don't see how that gives the religious answer any more credibility. It just feeds a more human need for answers of a certain type.
Despite potentially pandering to human desires at the expense of accuracy on this question no religion, as far as I am aware, has fully or satisfactorally actually answered the question of 'why' anyway.
Furthermore, for some reason everything else in the world has an answer to the question why?
Even religion can only provide limited respite from the question 'why' as eventually unanswerable questions about Gods motivation will always arise.
E.g.
Q: Why did God create the universe?
A: So that man could exist
Q: Why did God create the existence of man?
A: So that we could worship him
Q: Why does God wish to be worshipped?
A:
Edited by Straggler, : No reason given.