Do the contemporaneous sources speak about the author meeting him personally or merely of hearing about him? Because in 2000 years time, someone might read my teenage diary about having seen ET and conclude that aliens definitely exist because "Scorpette The Wise saw an extra-terrestrial"
'Contemporaneous accounts of seing [sic] JC's birth records'. Popped down the local registry office to ascertain it, did they? Did they get a photocopy we can look at? As you say, Christians at the time claim this. Does not mean that they did at all, seeing as their agenda demands that they insist they did. And again, there is the whole issue with Jesus being the most common man's name at the time going on there (and his parents having v common names, occupations and backgrounds). This is self-protecting propaganda that is instantly dismissible as any sort of fact.
Just because someone's university says that most people accept he existed doesn't mean that he really did!
There is a small amount of evidence but it is flimsy and from thousands of years ago, the stories have been written and rewritten so many times that no-one knows what was in the original stories anymore (for ex., Mary was not a Virgin in the Bible until a few 100 years ago - 'strangely' coinciding with a new Catholic and therefore social obsession with female chastity and sexuality at the time of a new edition of the Bible) and no-one wants to accept that it might all be hearsay, myth, half-truths, assimilation of many facts and people, made-up stories foolishly taken as truth and plain old flim-flam. Logically, no-one can state that there is 100% proof. If the same levels and types of evidence were used to prove 100% that another figure lived at the time - a figure that has no emotional investment for anyone involved in the research or the society funding it - the conclusion would have to be that they cannot prove it.
People are free to believe what they want. I put my belief in logic and provable facts and there is simply not enough proof that 'THE' Jesus definitely existed, end of story. And logically, the things he's supposed to have done and been are absolutely impossible, unfeasible and ridiculous.
I think that lazy assumptions, lack of questioning, illogic, unquestioning conformity and acceptance (and lies) are deleterious to the individual and society as a whole. Wanting to believe that Jesus definitely existed or believing it because that's what everyone's always been told doesn't mean he did exist.