None of them were written contemporaneously. Flavius wasn't even born until AD 37 and wrote about legends he'd
heard 70 or more years after the crucifixion.
The problem with proving a historical Jesus is the very nature of the subject matter. Any relics we might expect to find were made of wood, ceramics or bronze. Wood, if not preserved, deteriorates completely over time. Where are the ceramic and bronze artifacts? The ossuaries with "Joshua" on them are sketchy proof since it was a very common name during that period - much like "John" is today in western countries. Coulda been THE Jesus, but probably not.
"There's no evidence" isn't the same as "you can't prove it". It's more like Sagan said: ""extraordinary claims require extraordinary evidence" and looking at a very distant time in history after so much has been lost or destroyed, it's something we can probably never actually prove.
I'm merely demonstrating that none of the evidence believers point to is actually incontrovertible. He didn't leave a written record himself - he relied on his disciples to write many years later. Had he been a famous author on the NYT best seller list (in his day), this would be a different discussion. But he wasn't and here we are.