Without time, without causality, even at the point of a singularity, it is still logical to ask "Why is there something rather than nothing?" "Why does the universe exist?" These questions remain.
And they cannot be answered.
In actuality, there is no logical segue way from the singularity to asking why there is something rather than nothing. Existence does not require a temporal component. Asking 'why' is also not really a valid question in that circumstance as you are now getting into philosophical constructs versus physics-based assertions. 'Why is there something rather than nothing' or 'Why does the universe exist' are along the same lines as asking 'why do I exist'. It is a question assuming that existence requires a purpose of some sort. And in actuality, existence is not in anyway predicated on the notion of any sort of purpose.
If you are asserting that the philosophical questions themselves cannot be answered, that is due to the ambiguity of the question itself and the fact that it is attempting to apply meaning to a mechanism that is not necessarily meaning-based.
Note that these statements are common in religious circles in the realm of 'why did god allow my loved one to die' or 'why did god let me get sick'. Once again, they are attempting to assert meaning or purpose to a specific situation or idea, but they don't, in and of themselves, have any absolute proofs. Which is why the response is often 'the lord works in mysterious ways'. The answer is just as ambiguous as the question.
Pertaining to the discovery around the nature of the universe, it is far more logical to assert the concepts of randomness and chance. Since we already know that quantum mechanics is chance-based, the nature of the universe and how it manifested from a previous state is more akin to a random event as opposed to any purposeful event.