I normally start the sort of discussion you seem to have in mind with a subject that both Science and religion agree on. There was a Creation. The difference between the two is how that happened. The Science says it was a Big Bang. Science has no idea what caused the Big Bang. Christianity says it was God. So now we are indeed in an ‘OR’ situation, it is either one on the other, it cannot be both, though the possibility that God caused the Big Bang cannot be excluded.

As it happens, I believe that I can prove that the chances of us being here by the current scientific account are so close to zero that there is no point in differentiating it from zero. Providing I can set up the publication I have in mind, I intend to put that post up within the week. If I remember rightly it is entiltled How likely is the Big Bang.