Does the Big Bang support God or replace God?

Neither, directly—though it's often discussed as though it must be one or the other.

The Big Bang is a scientific model describing how the universe expanded from an extremely hot, dense state roughly 13.8 billion years ago. As physics, it says the universe had a beginning; it doesn't itself say anything about whether a personal God caused that beginning. That interpretive step is philosophical or theological, not something the equations settle.

Interestingly, the priest who first proposed the theory, Georges Lemaître, was careful about this distinction himself. When Pope Pius XII suggested in 1951 that the theory confirmed the biblical account of creation, Lemaître—a working physicist as well as a Catholic priest—pushed back, arguing a scientific theory can't function as proof of a religious doctrine. Many Christians do see the universe's beginning as consistent with, even suggestive of, the idea of a creator. But that's a further inference beyond what the physics itself demonstrates.