The biggest problem anyone has, in approaching what can loosely be called "the origin of the universe" from a "logical" perspective, rather than a physics / mathematical perspective, is that it is really hard to get day to day "logical" thinking around the fact that the big bang actually created time. The concept of "before" the big bang is meaningless - like further north than the north pole.
And when you accept that, all day to day "logical" thinking of cause and effect goes out the window (in relation to the singularity at the heart of the big bang, anyway).
There is some theorizing being done, at the cutting edge of physics, which might provide the shape of an answer - but saying it doesn't make logical sense is, I'm afraid, meaningless. The universe doesn't give a stuff about our "logic".
And it may just be, that the answer to "why does the universe exist" is "why not ?"
Could there be any greater conceit, than for someone to believe that the universe has to be simple enough for them to be able to understand it ?