What I'm trying to say is that while there is no proof of god, there is proof of other stuff that contradicts him.
If I can just jump in here.
Firstly, nothing is proven. There is no actual proof of anything that contradicts the existence of God, only theories. There is no fact in the world, only theories which, with the necessary equipment can be disproved.
So, for example, there is a theory that we do not exist but are actually the holographic projection of light/radiation from the Big Bang (or something like that). Now, this is a theory which is just as credible as the Big Bang Theory.
So basically, it is theorised that we don't exist.
Now, on the original topic, to say 'How can you believe in God?' is really quite disrespectful of other users beliefs. Yes, the majority of people in these forums are Atheist (or similar beliefs), but that doesn't mean that everyone has the same view. A better way to state this question would be: 'Why do people believe in God' or 'What Causes people to believe in God.'
As a Christian, I believe in God. And to answer the question, I believe in him because I cannot see any other way that the universe could be created in the way that it is today. For example, look at a common ecosystem and food chain. Every biotic and abiotic thing lives (although abiotic features don't exactly
live together, not quite in harmony but in a relationship which enables them to survive. I find it hard to believe that such a complex system could be caused by a 'giant explosion.'
Also, I have experienced things that cannot be explained by science, things like almost instantaneous mood changes during prayer...and I know of people who have experienced physical miracles.
So I hope that answers your question.