The best we have is letters from a whole generation after his death

Not really even "letters". But literally 2 accounts. One we're attributing doesn't even mention the correct name at the time. Jesus was often referenced as Yoshua at the time... So why the fuck did the account call him James? And the second account doesn't mention a name at all.

Edit: I need to clarify something since my phrasing is self-defeating (on purpose)... "often referenced as Yoshua at the time" as believed by biblical scholars who are almost universally religious. But the point remains. If the information we have now doesn't line up with what the accounts state (or the bible)... then how much of this shit is just made up bullshit?

And the 2 accounts are Tacitus (116 AD)

Nero fastened the guilt and inflicted the most exquisite tortures on a class hated for their abominations, called Christians by the populace. Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius

and Josephus Flavius (95 AD)

Testimonium Flavianum
About this time there lived Jesus, a wise man, if indeed one ought to call him a man. For he was one who performed surprising deeds and was a teacher of such people as accept the truth gladly. He won over many Jews and many of the Greeks. He was the Christ.

And by the way... Josephus' account is under heavy scrutiny and is general considered unreliable at best... and downright forgery at worst. The wiki articles linked are a good read and well sourced.

A really damning case in my opinion is:

that although twelve Christian authors refer to Josephus before Eusebius in AD 324, none mentions the Testimonium.

So other early authors that were Christian referenced Josephus works, but ignore the one that actually mentions Jesus directly? That seems odd no? Almost like the work was fabricated AFTER 324AD.