To support a claim for Jesus’ authenticity, one must support a claim to the reliability of the New Testament. This is a long and complicated process which others have written about very successfully. Here are the basics of a mountain of scholarly research. Craig L. Blomberg, in his chapter The Historical Reliability of the New Testament, found in Reasonable Faith sums up the research in this way.
“The texts of the NT have been preserved in a far greater number and with much more care than have any other ancient documents. The authors of the historical portions of the NT-the gospels and Acts-are quite probably Matthew, Mark, Luke, and John, just as the church has historically claimed… it creates a better case than we have for almost all other periods and documents of ancient history and should, therefore, be given serious credence.”1
The biographies of Jesus, Matthew, Mark, Luke, John, and Acts, are well documented by an uncommonly high number of ancient manuscripts, written by eye-witnesses, or recorded from first-hand accounts of eye-witnesses. They were transmitted responsibly and accurately through the following centuries.
1 Blomberg, Craig L. Reasonable Faith: Christian Truth and Apologetics. Rev. ed. ed. Wheaton, Ill.: Crossway Books, 1994. p. 226