What can be proved is that Jesus of Nazareth was an historic figure. And this historic figure fulfilled hundreds of prophecies recorded about him hundreds of years before he was born. This authenticates both his office and his claims.

He claimed he would lay his life down as a ransom for mankind and the he would raise it back up again.

500 + witnesses saw him alive after his very public crucifixion... many of which were still alive when the Apostle Paul spoke of them and the resurrected Jesus in 1 Corinthians 15:6. To make a spurious claim with witnesses still living would be like someone today claiming JFK was ******inated with a cross bow rather than a gun... it would be disproved and ridiculed. Paul's claims were not. And ancient record keeping in those days was more than adequate to record such an objection if there had been any... especially when one considers the non-Christian historians like Pliny the Younger, Tacitus, Josephus, and so on who mention Jesus and the claims of Jesus without an ounce of despute.

There's your proof using even contemporary extra-biblical sources.