If God provided proof that he exists, then it would be logical to believe in him. The absence of proof leaves only faith for belief. You do not need faith if you have proof and vice versa. By God’s own choice, he can only be known by faith.
But why have faith in this particular God? If God won’t give us proof, what’s to stop us from believing in Allah or Zeus? To have faith is to deny logic. What alternative is there to logic? How do we think? Mindlessness is the absence of logic.
Would God really create intelligent beings just to require they abandon intelligence?