the most convincing piece of evidence are the simple men with nothing to gain undertake great difficulties to spread a message and a wise message you wouldn't expect peasants to have, like when people marvelled at Jesus for his teachings. If they have not witnessed the resurrection of Jesus Christ and lied about it, then they make themselves most vile in their religions views. they would undertake all that trouble, just to lie, turned themselves not riches but pains and suffering and, in the end, hell. so we can conclude they thought the message was real. But was the message real or an apparition? Here I have two rely on experts who say mass hallucinations are extremely rare. Now is it more likely God exists and Christ is risen, than mass hallucinations, which is extremely rare, to happen to many people for 40 days and 40 nights and for them to walk away with similar doctrine. with this in mind throw away your irrational scepticism and consider Christianity. His church prevailing for 2000 years, longer than any political institution, through great trials, the many miracles that cannot be explained such as Padre Pio, the resurrection of Christ, the apparitions of Fatima, exorcists, who lead overworked and humble lives, and claim witnessing many demonic activities that can't be mistaken for anything else ( an exorcist tells his story by g.amorth), all the prophecies fulfilled in the Bible, especially the ones concerning Jesus.
I recommend you read the beginning of John Gospel, it is very beautiful and it represents the reality of why people believe and disbelief God.