Proof looks like this:
All men are mortal
Socrates is a man
Therefore, Socrates is mortal.
That's a proof. It "proves" that Socrates is mortal. Evidence, on the other hand, is such that it tends to lead one towards a conclusion. If I'm investigating a murder, I might discover that the victim had a very jealous ex-husband. That leads me to suspect that it was the ex-husband who killed the victim. It's not proof, but it's evidence.
Now, there is no proof like the one above for God's existence. With the possible exception of the Ontological Argument, none of the traditional arguments for God's existence are valid on their faces. But, at least in my opinion, these arguments provide evidence for God's existence. The idea that the universe should have a cause might not proove that there's a God, but it gives one reason to believe that there is a God.
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"Die Deutschen meinen, daß die Kraft sich in Härte und Grausamkeit offenbaren müsse, sie unterwerfen sich dann gerne und mit Bewunderung:[...]. Daß es Kraft giebt in der Milde und Stille, das glauben sie nicht leicht."
"The Germans believe that power must reveal itself in hardness and cruelty and then submit themselves gladly and with admiration[...]. They do not believe readily that there is power in meekness and calm."
-- Friedrich Nietzsche
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