Its not that simple...
There is no survivng archeological evidence, but then any son of a carpenter is going to be hard to find.
Eyewitness accounts, well the oldest - Mark's Gospel may have been written in Rome around 50-65 CE. 30 years after the events, but some sugesst that they were written later. This collection of gospels are not what they seem and historians search, as yet just a theoretical construct, has been given the name "Q" (short for Quelle, German for "source").
It's a tempting idea. Mark is regarded as the earliest gospel and hence closest to Q. Of the 661 verses in Mark, only 24 aren't quoted in either Matthew or Luke. Matthew and Luke occasionally disagree with Mark regarding Jesus' words or the order of events, but they never both disagree on the same point.
The problem with Mark, it appears that was he was not 'the' apostle himself, was an associate of the apostle Paul for a short time, but the gospel bearing his name is (to some minds) is based on the preaching of Peter. It's generally assumed to have been the first gospel written, coming in right before Matthew at about 65 AD. So he was not an eye witness, but a associate of somebody who never met Jesus, writing about the words of somebody who had met Jesus?
The author of Matthew is traditionally held to be the tax collector mentioned in Matthew 9:9, sometimes referred to as Levi. However, Matthew borrows heavily from the Gospel of Mark. It's hard to believe someone who was in close contact with Jesus would have had to rely on secondary sources. Since this gospel has the most quotations from the Old Testament, sometimes going to ridiculous lengths to try to show that Jesus was the fulfillment of Old Testament prophecy, it's assumed that Matthew was written for a Jewish audience. There is suspicion that it might have been originally written in Hebrew, although only Greek texts have ever been found. Scholars differ on the composition date, but most agree on roughly 65 - 70 AD with a few placing at as late as 100 - 134 AD.
The Gospel of Luke and the Book of Acts are assumed to have been written by the same person, since they are addressed to the same individual, a Roman named Theophilus. The author was a doctor, Paul notes in Colossians 4:14. If Mark represents the teachings of Peter about Jesus, Luke most likely represents the teachings of Paul. Luke claims to have researched his material, but his dating, especially in the early chapters regarding Jesus' birth, is inconsistent with other sources.
The book of Acts can be seen as a sequel to the gospel of Luke, starting where the previous book ends. But where in the earlier work Luke needed to research the story, in Acts he is a character in it. He was a companion of Paul on his missionary journeys and was present during his imprisonment. In this sense, Luke had more first-hand experience of Paul than he had of Jesus. Both books were probably written after Matthew and Mark, probably around 65-70 AD but before the destruction of Jerusalem in 70 AD.
The Gospel of John differs markedly from the other three books both in tone and in some historical details. John does not follow the timeline in the other three and adds quite a few stories and details not found in them. For this reason, it's thought that John's gospel was not a child of Q, but a completely original work either by someone who knew Jesus directly or by one of his associates. The three letters of John found near the end of the New Testament are generally assumed to have been written by this same individual.
The identity of John has remained a mystery, although tradition has it that he is "the disciple that Jesus loved" mentioned in John 13:23. But here is a curious thing. In the entire gospel, John never mentions his own name (although he does mention other gospel writers). His purpose is to exalt the deity of Jesus. It seems out of character for him to pat himself on the back in that one verse, if in fact he was John the apostle.
William Barclay gives us an elegant answer. He states outright that even if John was not the direct author of the book, it was at least written under his authority. The book likely dates from about 100 AD, the last of the books to be written. If this dating is accurate, John would have been very old. Barclay posits that it was probably a group writing remembrances from John's fading memories, and it was they who described John as the disciple Jesus loved..
Christ is supposed to have been a Jew, and his disciples are said to have been Jewish fishermen. His language, and the language of his followers must, therefore, have been Aramaic -- the popular language of Palestine in that age. But the Gospels are written in Greek -- every one of them. Nor were they translated from some other language. Every leading Christian scholar since Erasmus, four hundred years ago, has maintained that they were originally written in Greek. This proves that they were not written by Christ's disciples, or by any of the early Christians. Foreign Gospels, written by unknown men, in a foreign tongue, several generations after the death of those who are supposed to have known the facts -- such is the evidence relied upon to prove that Jesus lived.
So we don't have an eye-witness account for him
How about historical contemporary litrature. let me just say that there are over 70 Jesus's at this time, in the historical records for Judea, but not one conforms to Jesus of Nazareths profile.
The Gospels know nothing of thirty years of Christ's life. What do they know of the last years of that life? How long did the ministry, the public career of Christ, continue? According to Matthew, Mark and Luke, the public life of Christ lasted about a year. If John's Gospel is to be believed, his ministry covered about three years. The Synoptics teach that Christ's public work was confined almost entirely to Galilee, and that he went to Jerusalem only once, not long before his death. John is in hopeless disagreement with the other Evangelists as to the scene of Christ's labors. He maintains that most of the public life of Christ was spent in Judea, and that Christ was many times in Jerusalem. Now, between Galilee and Judea there was the province of Samaria. If all but the last few weeks of Christ's ministry was carried on in his native province of Galilee, it is certain that the greater part of that ministry was not spent in Judea, two provinces away.