I agree that there is no way you can deduce from observing the universe what may have "caused" it to come into existence.
The only way we can know anything about that is if Someone from outside the Observable Universe chooses to reveal that information to us.
It is true that there is the General Revelation derived from observing what has been made that leads some to deduce that there must have been a Creator. But everything else that might be or is known about what is Not Observable can only be known if it is explicitly revealed to us.
RE: God and The Big Bang