That is as solid an evidence as you are going to get with any ancient figure, and the mention of lack of reference in other writings of the period is an argument from silence. This is a bad place to start building a case against the existence of a figure that outside his small group of followers was an insignificant figure; a no-name agitator that was unceremoniously executed.
In fairness, 'any ancient figure' didn't actually heal the sick, actually raise the dead and actually feed thousands of people with a basket of food, in addition to claiming to be God ('s son), actually having supernatural phenomenons happen at his death, actually being resurrected etc. When I say 'actually', I mean this is not supposed to be some David Copperfield of the first century, but the actual, real deal. So, in light of that, it is a little strange that there are not more extra-biblical writings about him, IMO.
If there were rock solid evidence of Jesus' existence, we wouldn't need to believe.
In fairness (again), if there was rock solid evidence of Jesus' existence, people would still have had to choose to believe if the miracles were real and not tricks, and they would still have to choose to believe he was the Messiah. So faith would still be a big part of it, but evidence would have borrowed more credibility to the story. So evidence would not be a bad thing for Christians.
Imo, the lack of evidence doesn't discredit this christian message.
It doesn't discredit many of Jesus' teachings, but if he didn't actually exist, or existed but was just a man, that would put a real dampener on the whole 'salvation through him' thing(!). But - lack of evidence, and rock solid evidence, both require faith in what he was said to be.
But if the entire Bible through-and-through was backed up with solid, physical evidence, and miracles were a little more prevalent in our day, then it would have been easier for skeptics to not be so... skeptical.
Personally I am currently undecided as to what I believe about the historical Jesus. I am - for lack of a better word (or maybe it is the best word) - agnostic about it.