Belief in God is rational. Everything has a cause. So unless there is a first cause, then you would have an infinite regress. And then nothing could exist. Therefore there must be a first cause. Therefore God, the first cause, exists. QED. (You could prove the first step a priori that everything has a cause by noting that nothing can come from nothing. This makes it a priori, not just an empirical observation).
The idea here is to limit the number of causes. I am not saying everything needs a cause. I am saying just the opposite. That there must be a limit or else nothing could exist.
The idea is similar to what you have in logic concerning the infinite regress.
The quantum mechanics that I am aware of does not say something can come out of nothing. Rather before something it measured it is just a probability.
For those it might be helpful here to look at this from the standpoint of Kant. Unconditioned realities exist but their character is part dependent on the subject and part on the object.
