I see no fallacy with my comment on the Big Bang. Yes, I assume, with good reason, that if we do figure out the answer that it will be a natural one. Why? It’s because any answer we do have for any question about the nature of the world — Where does the sun go at night? Do demons cause disease? — have ended up being natural answers and never super-natural ones. In other words, given the 100% failure rate of supposed super-natural “explanations” for anything, there’s no reason to think that the explanation for the Big Bang’s cause would not be a natural one. I’m reminded of Sam Harris’s challenge: “I challenge you to think of a question upon which we had a scientific answer, however inadequate, but for which now the best answer is a religious one.”

As for your P.S., yes, some theists do, in fact, believe there was a Big Bang, but many of them believe that God was behind it.