I’m not saying it’s improbable that the universe arose by itself. I’m saying it doesn’t make sense. To say that existence arose by itself is, I suspect, a bit like saying that a square can be a circle. It’s not probability that’s the problem with the statement, as if we had an infinite number of squares then one of them is bound to be a circle. It’s that the statement defies logic. It would be a “miracle” of a sort if a square could be a circle, just as it would be a “miracle” if the universe could arise from nothing, not because it’s unlikely but because it doesn’t make sense conceptually.
To me what makes more sense is the view that a ground of all being, outside of time and space, caused our universe to come into existence. We cannot understand the nature of a being outside of the universe and outside the chain of causality, but the fact that we exist is evidence that there must be one. It is the nature of the reality we inhabit that gives evidence that there was intentionality behind the act of creation, and therefore God.
I like Krauthammer’s quip that “atheism is the least plausible of the theologies”. But again, not because atheism has a lower probability - if that could be worked out somehow - but because it doesn’t make sense, whereas belief in God does make sense.