For what it's worth, and this won't make any difference to someone who has already made up their mind, the Bible is the most attested writing coming to us from ancient times. I don't have the information in front of me right now, but there are literally thousands of extant manuscripts attesting to the accuracy of the Bible, especially the New Testament. In the late 1940s the "Dead Sea Scrolls" were discovered. These scrolls date to the time of Jesus and contain an almost complete copy of the Old Testament.

As far as Jesus not being mentioned by contemporary writers, I can name three off the top of my head - Josephus, Tacitus, and Pliny the Younger.

The writings of Caesar, Herodotus, and many others have far less attestation to support their accuracy and authenticity but no one ever seems to question them. If those are accepted with very little evidence, why not accept the authenticity of the Bible with much greater, both in quality and quantity, evidence?

edit to correct spelling.