...but the little we do know is enough for us to either accept or reject him.
the phrase "historical record" is very vague. Many writings from history are religious documents...are those discounted too? I say that because I assume you arent accepting the Bible as a trusted source.
You should ask the Christians who reject the Gnostic gospels.
Religious documents have a different purpose than historical documents. One can assume Josephus or Pliny were trying to record events as they happened. On the other hand, the purpose of much of the New Testament is not historical so much as religously instructive. Very little written in ther first or second centuries can be viewed without a certain amount of skepticism.