I'm sure it gets murky the closer we get to Peter, but I've always wondered if the claims of apostolic succession held water under the scrutiny of historical methodology.
The claim of apostolic succession is a theological one, not a historical one, but we do know a bit about the history of the early Popes. u/talondearg had something to say about it in this thread from a few weeks ago. Not to discourage further discussion but this could be a good starting point for you.