That’s literally what first-hand evidence is: an account from someone who met someone irl - e.g. John, Peter, Luke, Mark, etc.
Also in that historical context, the fact that there are letters at all is somewhat astounding, if Jesus were just some rando. At the very least they seemed to think that He was important.
The letters were not written until later though - b/c why would they be, if you had John + Peter + Luke + Mark all in one room, why would they be writing texts / emails / chats at one another? They still wrote it within their lifetime though, so “a whole generation after his death” is disingenuous - time passed, but those people who met Jesus were still alive, and wrote the letters, thus making them first-hand recordings of fact.
Not that I’m advocating that you become a Christian over all of this, just wanting to get that part of the story straight:-).