Also, bear in mind that one should determine the "Big Bang theory" from a more colloquial meaning of the Big Bang as a singular event happening everywhere. The theory is built from two basic postulates, general relativity and the cosmological principle. The latter says that the universe is more or less the same everywhere on large scales at a given age. So since general relativity is a dynamical theory, you can take the situation that we currently observe and check that the dynamical story works out. Then you can extrapolate it back before we can see (before about 400,000 years old when the opacity became to great to see though), and check that that story also works out. With some key caveats (dark matter, dark energy, inflation) it does.
So all that is the "Big Bang theory." None of it refers to any creation event, or anything happening everywhere, because we're not sure how far back we can get away with our two postulates. We literally don't know if general relativity still works all the way back to the beginning, if the cosmological principle still applies, or if we have the idea right about inflation (for which there really is no confirmed theory at all). So astronomers apply "the Big Bang theory" essentially daily, without ever even mentioning how far back they imagine they can extrapolate it. For that reason, it actually isn't a theory about the beginning of the universe, though it is often mistaken for that.
By contrast, the Big Bang "event" is intended to be a creation event, but there's no scientific theory for it. It's more like a pop sci picture of what might have happened, that we really have no way to test at present. Part of the problem is that the scientific theory that we actually do have predicts an early phase that is a thermodynamic equilibrium with only tiny variations, of which we can only see a tiny part because it is thought to have expanded so much as to dwarf what we can actually see. It's hard to imagine a physical system that is better at covering its tracks than that!