John HSOG said:
God's existance does not depend on his followers being able to prove the fact.
Very good.

The same goes for the non-believers: simply because science hasn't solved
ALL the mysteries in the universe, doesn't mean that the universe's existance depend on science
I think that from this thread's title you should be able to understand how the non-believers think:
1) Believers CAN'T prove the existance of god. That is a fact. You can prove something only when you have evidence. e.g.: you can't arrest someone for a crime without evidence/witnesses.
Non-believers can't claim that they know everything about universe's creation(because, to accept something, they want it first to be proven), BUT, they can claim that they have evidence(to a certain extend) for their "god".
Using my logic, I'd say, the previous leeds to a second question:
2) If believers can't prove the existance of their god, how is it possible to believe in him? With their feelings? With what they've been told? With reading a book like the bible? What about all the other billion people in the world who also claim that their god is the real one and many of them claim that they saw him? Are they wrong? If a Christian had been born in China he would believe in Bhudda and vice versa. Nothing of the previous can be proved.
I think that the believers rely too much on their feelings/emotions. If we put aside our logic, what makes us better than the animals? Sure, we also have feelings and emotions(because, IMHO, we're animals with feelings and emotions and logic), but only using a logic path we prevailed against animals, discovered writing, medicine, science, space ships and so on...