What is the source of Faith?

"Faith cometh by hearing, and hearing by the Word of God"

Romans 10:17

Here's the mystery: 

Those to whom some of the greatest signs were shown, still failed in unbelief. The children of Israel walked through the Red Sea and then saw their enemies drowned. But when put to the test, they forgot what God had just done, and started complaining. So there is no connection between miracles and belief. Jesus said “Even if one rise from the dead, they will not believe “. He did rise from the dead, and sure enough, many did not believe. 

For me, belief in the existence of God is teleological: The end declares the means. However, even if one clears this hurdle and admits God must exist, that is not belief as the Bible defines it. This comes from hearing the Word of God and trusting Him.