Saint Peter and Papal authority

When Jesus conferred the Keys to Simon, he created not just the office of the now-named Peter, but the Church itself.

That Peter was the leader of the Church is indisputable, from his far more numerous mentions than any other Apostle in the Gospels, to descriptions of his leadership in Acts, and, of course, his establishment of the seat of the Church in Rome.

But how do we know that Peter conferred the office to a successor? Instead of some type of declaration, "I am the Pope, and my successor is Pope," etc., what we have, instead, is marvelously simple: a complete absence of any discussion about it. The Seat of Rome was from Peter onward through to later schisms, the assumed seat of the Church, and all pronouncements, orders, encyclicals, etc. came from it without objection from anyone else.