On the subject of why God doesn't reveal himself, I'll say this:
First, if he did there'd be no free will. It's similar to walking into a bank when the full SWAT Team is standing with weapons aimed and trying to pull a stick-up. You know you have no chance, so you wouldn't even try.
Second, most atheists present God with a challenge out of arrogance. "Show me some tricks and I'll believe in you". God doesn't need anyone's belief. And if you were the all-powerful creator of the universe, would you humble yourself to some insignificant weasel demanding you placate them?
On the other hand, if you go before God with humility and an open heart and mind, he will reveal himself to you. Maybe not in the way you'd like, but he will. It's certainly been the case in my life.