|... it is known that some texts have been corrupted over time, or have been changed by unscrupulous copyists. Thus, it is not always possible to separate later interpolations from the original writings. ...Second of all, some texts have been lost, and are only known through quotations in secondary sources. In addition, not only have some alleged references to Jesus been lost as primary sources, but some early criticisms of Christianity were suppressed by the early Church and no longer survive. Furthermore, of the surviving texts, both pro-Christian and otherwise, many texts cannot be dated with precision, or survive in more than one form. ...
A reader of the ancient texts is struck by how little the literature has to say about events in the New Testament. For example, Herod's infamous murder of the Innocents...
... if a writer is merely repeating what he was told by Christians, who in turn derive their information from the New Testament, then the text in question does not provide independent confirmation of the New Testament, as the claims involved are ultimately derived from the NT. An example of what might constitute independent confirmation would be an eyewitness account by a non-Christian author, or an entry in a Roman legal document...
If we had to prove the existence of anyone from the Roman World through the existence of a legal document, we be unable to prove that almost anyone existed. As for eyewitness accounts, even the histories of the Caesars are full of contradictions.
Leaving aside the miracles for a moment, can we prove that Jesus existed through a non-Christian source? Probably not. But to prove that Jesus did not exist would require one to disprove the historicity of the Christian sources. I don't think that this has been done.
Our understanding of the times of Christ are often influenced by what Christianity became later; Big, Organized, and Produced by Cecil B DeMille. Since Christianity is big now, we are looking for signs that it was big then. But it wasn't. At one point it was one poor carpenter and some guys. One can accept this or not. But at its origins, it just wasn't on the radar screen. One can believe the Bible or not, but not only do we not have outside evidence for miracles, the people who were there to see them weren't seeing them either. Fact is, to Rome and to the local authorities in Jerusalem, Christ was a petty criminal and a heretic. Not worth anyone's notice. So I think we should be surprised if He appeared in the same chronicles that were documenting Tiberius or Claudius.
One of the biggest historical mysteries is how Christianity expanded so quickly. If it was through a conspiracy, it was a conspiracy of illiterate fisherman in a backwater country where Romans were sent to govern as a punishment. Yes, there was Paul, the Roman citizen. But who was he? He was a nobody too. I know that the spread of Christianity doesn't prove that Christ existed. But it doesn't support the idea that He was concocted either.
I suppose that we don't have much more evidence for the historicity of Christ than we do for any other common inhabitant of the Roman Empire. We have a succession of early popes whose names we hardly know; yet no one is claiming they don't exist. Almost all the evidence is in the Christian texts. And our historical (as a science) support for Christ in these texts comes from the application to them of modern historical and archeological methods. Not much more to say.
If you want to get more controversial about this (and maybe provoke a more interesting discussion), start a thread with a topic like "If it turned out that some of the Bible were not factually true, would Christianity immediately come crashing to the ground?"