Where did Jesus ever say to go out and prove that God exists?

If he existed, he most likely didn't say that. He would most likely have known that it would be impossible and so did the writers of the Bible. That's why the Bible is full of thought-terminating cliches like "The fool says in his heart 'there is no god'", etc. etc. It's an old trick: if you can't prove your point, the best you can possibly hope for is to make anyone believing the contrary look like a fool.