Strictly speaking, we do not yet have a theory for what triggers the big bang, but we have a theory (or theories) for what happens shortly after the big bang.

What happens right at the big bang demands a theory that unifies the quantum mechanics and space-time (general relativity), which is still under development. But shortly after the big bang, the universe starts to cool down, and the quantum nature of space-time no longer matters, then our current theories for physical laws such as general relativity and particle physics can well describe the expansion of the universe, and formation of galaxies.