Hue-man, I think you've wasted your time trying to prove Jesus did not exist (BTW, you ought to get your own history right before criticizing "believers" . . . Mark, a companion of Peter, and Luke, a companion of Paul, were not apostles). But my main criticism of your historical critique is that you apply your analysis narrowly, ignoring anything that supports Jesus having lived, and then paint a one-sided picture clearly intended to take a stab at the religious. (Just so you know my bias, I am not religious; so nothing I say is meant to defend Christian belief.)
I say you waste your time because I suspect the historicity you really doubt is the miracles of Jesus
. Really, if it weren't for the supernatural claims followers have linked to Jesus, would you go to all the trouble to disprove he existed? This common strategy of the atheist or anti-religious seems to conclude that if one can get rid of Jesus then we get rid of any rationale for Christianity. There is, of course, another logical possibility and that is that Jesus existed, but his followers made up the supernatural stuff to help convince a very superstitious population that Jesus was from God.
Getting back to what's wrong with your critique, traditionally history has been based on written documents; since some events really happened that weren't written about, and because there are those who write things with spin (even witnesses) to present a picture to support some ideology, written documents may or may not be an accurate representation of the facts.
The more recent field of prehistory
has produced some great evidence. A painted clay pot found in ancient Mesopotamia proves they knew pottery and painting. Do we need written documents to confirm that? No.
Another source of records (notice I didn't use the term "history") is myths. The story of Noah for example, is also known to be similar to a Babylonian flood story in the Gilgamesh myth, and of course Jewish records tell us that the Jews were in Babylonian captivity for a time. Over 2500 years later two oceanographers, Dr.s Pitman and Ryan, find evidence of the collapse of the Bosporus strait causing the Mediterranean to pour into the Black Sea. Follow up investigations find clear signs of culture buried under the Black Sea dating to the time of that devastating flood. A link to the book: Amazon.com: Noah's Flood: The New Scientific Discoveries About the Event that Changed History: William Ryan, Walter Pitman: Books
Besides archeology and myths, there are more important indicators of past events, and that is influences found in people alive today. Genetics, for example identify our ancestors, and even indicate such seemingly impossible to verify facts like homo sapiens interbred with Neanderthals. Do we have any written records of cross-caveman romances? Nope. Yet another type of past influence is found in language, as the great work of Franz Bopp demonstrated through his comparisons of the Indo-European languages. Can you believe that English and German were once the same language, and that the languages came to differ by segments of an original common population splitting off and moving away?
Are there other past influences alive in us today? What about the passion for reason the Greeks gave the West, the passion for studying the effects of polar forces given to the Chinese by early enthusiasts like the Duke of Chou and Confucius, the passion for looking inward so revered by the Indians after first developed by the Buddha and many other early practitioners, etc. And this brings us to Jesus. Can we see an "influence" alive today that indicates a past source?
As much as you may dislike religion, what do you think made Rome turn from thinking a fun Sunday afternoon was watching people get eaten by lions, to living with more compassion? Greco-Roman culture greatly influenced European culture, and America derived from European culture. Can you imagine what views we might have toward our fellow human today if Constantine hadn't declared the Empire Christian some 1700 years ago?
Of course I don't know whether we might have come to more compassion without those Christians who bravely prayed while the lions ate them and so through that act of faith moved many Roman spectators to compassion. But it does seem that without some sort of influence
to give them such faith, they would not have behaved so.
My point is that while we might not have definitive written records, we do have an influence that dates from the time of Jesus, and that influence seems to inspired early followers to bravely face death (just as Jesus is reported to have done), and to stand up for love and goodness (again, as reports say of Jesus). And before this influence, look at what was going on. Something
changed the normal behavior of people at that time, and since all those reports claim it was the personage of someone called "Jesus," what better evidence do you have for this influence? None I've heard.
If you want you can ignore all the good people do and have done from that influence, and point to the excesses and silly beliefs of some religious, but that isn't a fair presentation of all
the evidence. Further, there is no reason to assume that Jesus wanted "religion" to develop at all; to the contrary, the reports we have show him a religion iconoclast, which is in fact exactly what got religious leaders of the time plotting against him!
In conclusion, I'd suggest a better way to spend your time is proving supernaturalism is nonsense . . . and leave Jesus be.