In terms of scientific or mathematical proof, you cannot prove the existence of God. Scientific Proof is a series of logical steps which are irrefutable. God however, unsuprisingly, is beyond human logic, as it says numerous times in the bible.
For the wisdom of the world is foolishness in God's sight - 1 Cor 3 vs 19
for example.
However, science can lead to a necessity for God, if no scientific explanation for what is experimentally obseved can be achieved. Take for example the cause of the big bang, and the existence of time itself. More importantly, there is spiritual proof, which guides millions of Christians worldwide. You might not be able to explain it, perhaps it is "spiritually discerned", but it provides a more than sufficient answer for most Christians.
Nick