I realize that I can't. And that's alright.
I cannot provide scientific proof of the Judeo-Christian God. I can argue God philosophically, logically, theologically. I can offer no scientific method-type proof that would satisfy. None whatsoever. Yet I believe anyway.
My atheist friends loooooooove when they get me to this position in a debate!
Although fictional, I always think of Ellie Arroway, the atheist scientist in the book/movie CONTACT, regarding the demand for proof of her supposed intergalactic journey:
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...I wish I could share that. I wish, that everyone, if only for one moment, could feel that awe, and humility, and hope. But that continues to be my wish.
A faith experience is very similar. I've had several experiences in my life that have confirmed the faith I was born into. When I received Communion for the first time. When I first met my wife. When I made my first Confession in 20 years. When I saw my sons leaving their mother's body into the world. When I decided to stop drinking, literally in mid-slug. When my cancer-afflicted mother asked for my prayers...and her doctors still can't fully explain her recovery.
In each of these experiences, God was with me. Period.
I can't prove it. I can't explain it. But like Ellie, everything that I know as a human being, everything that I am tells me that it was real. Thank you God, for Your Presence today and everyday, for believers and non-believers.
Daily Mass Readings