I don’t worry so much about “proof”. Tradition has always taught that that’s how St Peter left this earth, and since “tradition” is a handing-down, whether orally or written, I will believe tradition before I will believe what those who question history would try to convince us of.
There is a dangerous trend nowadays to question everything that’s been handed down - a revisionist view of all history that is not to be believed but questioned, and that only modern-day views (which really don’t teach anything concrete but only call into question and sow doubt) should be accepted, but centuries of belief cannot be cavalierly dismissed.
I’m nothing, but as for me, I prefer to believe the humility of tradition rather than the arrogance of modern ‘reason’. If there is written proof, great, but if not, centuries of believers can’t all be wrong.