You can't use science to prove the existence of God. The only two ways that I am aware of is the one I put on the top on my blog:  
 Everything has a cause. So unless there is a first cause, then you would have an infinite regress. And then nothing could exist. Therefore there must be a first cause. 

The other way is by a proof called the Ontological proof. That is God has all possible perfections by definition. If he would lack existence he would lack one perfection. Therefore He exists. This was put into rigorous logical form by Godel.  I saw this once in Hebrew University and later someone put it on the internet.  This seems to be good but I prefer the basic idea of the First Cause. 

The basic question on the ontological proof was stated by Kant that existence is not a predicate. But we know that "is" is in fact a predicate. But what Kant means to ask is really that logic can not penetrate into unconditioned realities. He is asking a question based on his entire way of thinking--not just a minor observation. And we know that people after Kant have tried to bridge this gap. 

However I think this goes too far into theology. I do not want to assume characteristics of God. Nor did the Rambam. It was enough for him to borrow from Aristotle's First mover to get to the First Cause and that is enough for me. In fact, I would prefer not to assume any characteristics about God at all. I go in this way like the Book of Job. In that book the friends of Job said God is just and we can not understand his ways. The normal Shabat Table Judaism standard fare. But at the end  of that book God comes along and says the friends of Job were wrong. This same point was driven home by Schopenhauer who basing himself on Kant thought that God is the ding an sich--wild, delighting in being unpredictable, with no interest in being considered good. The Will. And the world is just an expression of the Will.