Though the term pope wasn’t used way back then, St. Peter knew he was head of the Church. He was the apostle who “shall be called Cephas(Peter)”. Jesus founded his Church on the foundation of Peter, the rock (Matthew 16:18).
Scripture indicates it is Peter that is the primary over the apostles. It is he who has authority over the others and the early Church.
Whenever they were named, Peter headed the list. Peter was the one who generally spoke for the apostles (Matt. 18:21, Mark 8:29) Peter preached to the crowds on Pentecost (Acts 2:14-40), and he worked the first healing in the Church age (Acts 3:6-7).
It is Peter’s faith that will strengthen his brethren (Luke 22:32) and Peter is given Christ’s flock to shepherd (John 21:17). He headed the meeting that elected Matthias to replace Judas, and he received the first converts (Acts 2:41). He inflicted the first punishment (Acts 5:1-11), and excommunicated the first heretic (Acts 8:18-23).
He led the first council in Jerusalem (Acts 15), and announced the first dogmatic decision (Acts 15:7-11).
Read what an early Christian had to say on St. Peter’s role in the Church and his successors.
Cyprian of Carthage, an early bishop of the Church, wrote this in AD 251.
“The Lord says to Peter: ‘I say to you,’ he says, ‘that you are Peter, and upon this rock I will build my Church.’ . . . On him [Peter] he builds the Church, and to him he gives the command to feed the sheep [John 21:17], and although he assigns a like power to all the apostles, yet he founded a single chair [cathedra], and he established by his own authority a source and an intrinsic reason for that unity. Indeed, the others were that also which Peter was , but a primacy is given to Peter, whereby* it is made clear that there is but one Church and one chair****. So too, all [the apostles] are shepherds, and the flock is shown to be one, fed by all the apostles in single-minded accord. ***If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith? If he [should] desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church?” *(The Unity of the Catholic Church 4; 1st edition [A.D. 251]).