Yes, my "independent proof" was independent of the existence of the universe. There are several hundred or several thousand proofs as a matter of fact--the answered prayers I've had since I was converted in 1971. I also consider my very conversion to be proof of God. Why would I, a dedicated agnostic, become convinced of the existance of God without the existance of God? I had no motivation to become converted. My parents were not Christians and I was not a church goer.
This leads to a good experiment for the sceptic. Test prayer in Jesus' name. See if anything changes in your life. I'll happily pray with you. We'll see what happens over 6 months times. The control can be another sceptic who doesn't pray, or who prays to some other deity.
Hospitals are full of people who are dying horrible deaths, and who cry out in Jesus' name. Their families pray with them. And their whole churches sometimes join in. Yet they die. By the millions. By the hundreds of millions. Year after year, century after century. I'm happy that you've found Jesus, and that things are going so well for you in your life, but I don't think the totality of of the evidence proves anything at all.