Logic is subject to human undertsanidng and comprehension and evidence should be demonstrable. You said God is subject neither to logic nor provable evidence. Besides, one must be able to define what it is he believes in. Evidently, that's not possible either. So, what's left?
God is not so subject. But we are, if we're rational. Indeed, our rationality is itself evidence of our subjection to and dependence on God; i.e., His Logos.
I see evidence of God everywhere; but this is not the sort of evidence that can be directly observed and scientifically measured. Which is what you are asking me to provide.
The evidence that I find most persuasive is the seemingly perfect correspondence among God's four revelations: Holy Scripture, the Incarnation of Christ, the world of Creation, and the Holy Spirit with us.
But this is the very sort of evidence which is unacceptable to you. More, it's the very sort of evidence you want most to tear down, disqualify.
So, what do we have to say to each other, really? We can't even get on the same page.