I'm a Protestant with doubts from church history. What is the best way to establish the truth of the papacy?

Well, I think the best way is to see or acknowledge the fact that we've never had a break in the papacy. It starts from 33 AD with Peter and then goes completely undisturbed, except for maybe one instance where we had three popes at one time. But that wasn't because we didn't have the true Pope. We just didn't know who the true Pope was. This is in the 1300s. We found out who it was and we went on from there. That says something: this is not an earthly thing. This is something that heaven is behind because of that purity. We're just saying the longevity of the papacy is a good reason to know that this is something supernatural. This is not something man can do. If left to man, the papacy might not have lasted for three or four men, much less the 266 that we have. So that's the best way to look at it, if that helps you.