Your questions "Do you believe in the Big Bang theory?" and "If yes, what convinced you that this is how the universe came to be?" imply that if there is a Big Bang, then this Big Bang is how the universe came to be. But that's not the case.

General relativity theory is a proper description of spacetime, and GRT includes singularities like the center of black holes and the big bang singularity. So the Big Bang is real, indeed. It is a misconception, though, that spacetime comes into existence via the big bang. Spacetime, including it's laws, and including the Big Bang, is emergent from more fundamental objects and laws that we describe by Quantum Mechanics. (The Copenhagen interpretation was a philosophical belief system that denied this and made up some nonsense about collapsing wave functions, but all that's left of that deeply unscientific bullshit today is the attitude "shut up and calculate" of some really bad college text books.)

To apply the scientific method about the question how the universe came to be, you have to mathematically model how spacetime emerges from quantum mechanics and then try to falsify that model's observable predictions by experiments. If generations of physicists keep being interested enough in failing on that subject, you can finally consider it knowledge. This is why we know that GRT is a proper description of spacetime and therefore that the Big Bang exists. But we're not there yet about spacetime emergence from quantum state. We have some very plausible theories but not enough conductible experiments to observe that reality manifests in that ways. And without experiment it's just belief. Even in science.

In short: We don't know how the universe came to be. But we know that it just includes a Big Bang and did not originate itself from one.