I am flattered INKLING!
The Leap of Faith is all there is I am afraid.
As far as the "proof" for God's existence, I cannot offer you that (well logical/philosophical proofs perhaps but nothing like what a scientist would require). I think believing in God requires a leap of faith. However I do believe that there is enough evidence from which one can reasonably draw a conclusion that God does exist--or not, depending on how you view the evidence! God isn't the only thing we take without evidence. Take Hume's induction problem for example. There are many other examples of things we believe without evidence as we go about our daily lives and are inherent in scientific inquiry that are nonetheless "reasonable".
When it comes to the the existence of God, the Bible (I hope I don't sound like a Bible thumper) says that there are people who have seen sufficient evidence, but that they have suppressed the truth about God. On the other hand, for those who want to know God (if he is there) he says, “You will seek me and find me when you seek me with all your heart. I will be found by you,” declares the Lord, “and will bring you back from captivity.”
As for me, I believe God exists. When you look at how incredible our universe and world is...sitting in front of the stars in wonderment...resolving my first planet as a boy with a telescope my Grandfather gifted me..... the complexities of the human body right down to our genetic code....my own son.....I think it is more reasonable to conclude that the results are that of a Creator as opposed to a roll of the dice.
and what does it feel like?
This movie quote from Contact (based on the Carl Sagan book which I recommend), made by an atheist character, Ellie Arroway, comes very close, I think:
I... had an experience... I can't prove it, I can't even explain it, but everything that I know as a human being, everything that I am tells me that it was real! I was given something wonderful, something that changed me forever... A vision of the universe, that tells us, undeniably, how tiny, and insignificant and how... rare, and precious we all are! A vision that tells us that we belong to something that is greater then ourselves, that we are *not*, that none of us are alone! I wish... I... could share that... I wish, that everybody, if only for one... moment, could feel... that awe, and humility, and hope. But... That continues to be my wish.
BurnTheShips