The difference is how we arrived at the realisation. Big Bang is by scientific method, looking to be improved or proven wrong. And God is through stories that somebody just made up.
The Big Bang scientific theory is how it happened. God, Hawking's quantum fluctuations in the metaverse, etc. is what caused it. They are completely unrelated.
Also, science has nothing to say (no falsifiable theory) about what caused the Big Bang, unless we find some way of observing outside the universe. The argument by Judaism/Christianity/Islam is that an entity exists outside of the universe (God) and has communicated with us, and said entity asserts to having made the universe. Presumably via the Big Bang. The stories might be made up, but then again, it is possible that some of them might be true. However, unless God acts consistently over repeated observations (unlikely), you will have to use a different way of evaluating truth than science.
