You have a mistaken notion of the Catholic term mystery. A mystery is not something about which can’t know anything, but something about which we can’t know everything.
God gave us brains and expects us to use them to understand the mysteries of faith, to the extent such understanding is possible. That total comprehension isn’t possible doesn’t mean you have to “check your brains at the door” anymore than failure to entirely grasp quantum physics does.
There’s no real opposition between truths of reason and truths of faith, only an apparent one. When scientists propose as fact what is only an unproven hypothesis, or when theologians mistake their personal opinions for articles of divine revelation, the impression is left there’s a conflict between the two realms, but this isn’t the case. It only appears to be so because someone has erred.
Faith tell us more than we could know by reason alone, but it can’t contradict reason. Furthermore, we can use our reason to better understand our faith. In fact, that’s a classic definition of theology: Faith seeking understanding.