timojin:
The quarks were there before the universe had cooled enough for them to combine into particles like protons and neutrons.
When quarks in the early universe combined to form protons etc., that process did release energy, as you say. However, the universe was expanding rapidly enough for the average energy density to be falling despite this energy release.
You ought not to judge it until you understand it better. Try to keep an open mind.
The thing that makes the big bang more plausible than Creation is that the big bang theory matches (and explains) what we actually observe today when we collect data from the universe. In constrast, Creationism is a fraud that ignores a lot of the accumulated real-world data that has led us to our current scientific models.
Regarding hand-waving: it is inevitable that you will not get all the details about the big bang theory on a forum like this. To get a really good understanding, you'd need to learn quite a lot of physics at university level first, then study textbooks, research papers etc. What you get on a discussion forum is descriptions that try to give you a feel for what the theory says, but don't mistake what you get here for the theory itself. The theory is mathematical, quantitative, based on actual observations, and so on. It is in no sense "hand waving".