Based on what I've been gathering, there is no way to prove or disprove the existence of a god/deity in theory.

If people define a god to be completely unfalsfiable, then yes.

The problem, though: is believing in such things justified? I don't think it is.

science struggles to prove the big bang based on the law of the conservation of mass.

The Big Bang is not about the beginning of the universe, and is instead about the rapid expansion of the universe.

The Big Bang did happen, as we have strong observational evidence for it. The details of how it happened are still being worked out, but, like other scientific theories, the Big Bang model makes testable predictions which continue to be confirmed. In short: the Big Bang model is the best explanation for the observations we currently see.

I know this also relates to the creationism theory hypothesis and questions how plausible it is, but one must keep in mind the limitations of each view.

Creationism is a hypothesis. It is not a theory in the scientific sense. The way you're describing things, it sounds like the scientific concensus is an opinion or unsubstantiated position - it's not. One of these "views" has an overwhelming amount of evidence to support it and makes testable predictions which come true, while the other does not.

If you have not seen it yet, definitely check out Aron Ra's series titled The Foundational Falsehoods of Creationism. He makes an excellent case for a definite pattern of deceit and wilful ignorance.

At the end of the day, all that the debate really boils down to is personal choice based on what we already know and what we can assume we don't know.

You're wilfully ignoring evidence, then.