Forget the proof of God for a moment and explain why should non-believers want to know God?
Somebody could define 'God' in the more philosophical manner, as first cause, designer, ground of being, unchanging source of Platonic universals, ultimate goal, pure goodness, and so on. In that case, 'God' would be kind of a personalized anthropomorphism of whatever the unknown answers might be to many of humanity's largest and most fundamental questions. So part of your answer would be curiosity, I guess. People, many of them, have a deep, innate and probably instinctive desire to
know.
I'm more cerebral and academic than most people and prefer to address these kind of questions with science and philosophy. But the motivation isn't all that dissimilar. If you're old enough, think back to the atheist Carl Sagan displaying beautiful photos of the glories of the cosmos on his TV series while solemnly intoning "billions and billions..." That was his sense of transcendent possibility.
Religious people feel similar things, but they tend to stick to the conceptual vocabulary of myth and tradition and they always seem to feel driven to personalize it. They don't just want to
think about ultimate things conceptually, they want to
feel them emotionally, they want to love and be loved by them, they want to embrace them and
be embraced in turn. They want to return to the unquestioned love and security of a child in its parents' arms.
They want escape from all their doubts, worries and suffering. They want to escape the inevitability of death. They want salvation.