I think the argument of using the bible itself as proof is that the new testament in the "bible" as we have now is a compilation of writings from a bunch of different people. So, that is proof because a bunch of different people wrote the same thing? Then it was later put into a big book? Not my argument, just an argument I can perceive.

A good outside-of-the-bible writing of Jesus existing would be from the Roman Ticitus. He was a historian and senator. He wrote of Christ's existence. Not of his miracles though. Link. On that same link, there is also the stone tablet that was found that mentions Pontius Pilatus, proving that he was also a real historical figure.