Yup, but then Peter died.
But the Church believe God’s mercy is greater than we know (thankfully). It’s called ‘baptism of desire’. Think of the good thief on the cross, He was saved without it. The Church also believes that God takes care of those who have never heard of Him. Like some guy living in Outer Mongolia. Ulimately, God is still the judge, only God knows what is in men’s hearts.
Or maybe the only Baptism that really matters is the Baptist of the Holy Spirit.
Peter might have died but not the authority of the Papacy. All his successors that occupy the chair of Peter have the same mandate.
Irenaeus
“The blessed apostles [Peter and Paul], having founded and built up the church [of Rome] . . . handed over the office of the episcopate to Linus” (Against Heresies 3:3:3 [A.D. 189]).
Tertullian
“[T]his is the way in which the apostolic churches transmit their lists: like the church of the Smyrneans, which records that Polycarp was placed there by John, like the church of the Romans, where Clement was ordained by Peter” (Demurrer Against the Heretics 32:2 [A.D. 200]).
The Little Labyrinth
“Victor . . . was the thirteenth bishop of Rome from Peter” (The Little Labyrinth [A.D. 211], in Eusebius, Church History 5:28:3).
Eusebius of Caesarea
“Paul testifies that Crescens was sent to Gaul [2 Tim. 4:10], but Linus, whom he mentions in the Second Epistle to Timothy [2 Tim. 4:21] as his companion at Rome, was Peter’s successor in the episcopate of the church there, as has already been shown. Clement also, who was appointed third bishop of the church at Rome, was, as Paul testifies, his co-laborer and fellow-soldier [Phil. 4:3]” (Church History 3:4:9–10 [A.D. 312]).
The Baptism of the Holy Spirit is what we all the Sacrament of Confirmation.