Your own linked document tries to use Josephus to discount Herod's killing of the Jewish infants. Yet here is what Josephus says about Jesus. Here we have a contemporary writer , not one generation removed from the story, historical figure claiming that Jesus is the Christ

3. (63) Now, there was about this time Jesus, a wise man, if it be lawful to call him a man, for he was a doer of wonderful works-a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews, and many of the Gentiles. He was [the] Christ; (64) and when Pilate, at the suggestion of the principal men amongst us, had condemned him to the cross, those that loved him at the first did not forsake him, for he appeared to them alive again the third day, as the divine prophets had foretold these and ten thousand other wonderful things concerning him; and the tribe of Christians, so named from him, are not extinct at this day.