The papacy was NON existent for the first few hundred years of Christianity...
This a proof proven over and over and over and over again...
That is an untrue statement. The first Christians speak out in opposition to what you have posted:
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]).
Cyprian of Carthage:
"The Lord says to Peter: ‘I say to you,’ he says, ‘that you are Peter, and upon this rock I will build my Church, and the gates of hell will not overcome it. ... ’ [Matt. 16:18]. 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. . . . If someone [today] 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; first edition [A.D. 251]).
"Cornelius was made bishop by the decision of God and of his Christ, by the testimony of almost all the clergy, by the applause of the people then present, by the college of venerable priests and good men, at a time when no one had been made [bishop] before him—when the place of [Pope] Fabian, which is the place of Peter, the dignity of the sacerdotal chair, was vacant. Since it has been occupied both at the will of God and with the ratified consent of all of us, whoever now wishes to become bishop must do so outside. For he cannot have ecclesiastical rank who does not hold to the unity of the Church" (Letters 55:[52]):8 [A.D. 253]).
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]).
Optatus:
"You cannot deny that you are aware that in the city of Rome the episcopal chair was given first to Peter; the chair in which Peter sat, the same who was head—that is why he is also called Cephas [‘Rock’]—of all the apostles; the one chair in which unity is maintained by all" (The Schism of the Donatists 2:2 [A.D. 367]).
Jerome:
"[Pope] Stephen . . . was the blessed Peter’s twenty-second successor in the See of Rome" (Against the Luciferians 23 [A.D. 383]).
"Clement, of whom the apostle Paul writing to the Philippians says ‘With Clement and others of my fellow-workers whose names are written in the book of life,’ the fourth bishop of Rome after Peter, if indeed the second was Linus and the third Anacletus, although most of the Latins think that Clement was second after the apostle" (Lives of Illustrious Men 15 [A.D. 396]).
"Since the East, shattered as it is by the long-standing feuds, subsisting between its peoples, is bit by bit tearing into shreds the seamless vest of the Lord . . . I think it my duty to consult the chair of Peter, and to turn to a church [Rome] whose faith has been praised by Paul [Rom. 1:8]. I appeal for spiritual food to the church whence I have received the garb of Christ. . . . Evil children have squandered their patrimony; you alone keep your heritage intact" (Letters 15:1 [A.D. 396]).
Augustine:
"If all men throughout the world were such as you most vainly accuse them of having been, what has the chair of the Roman church done to you, in which Peter sat, and in which Anastasius sits today?" (Against the Letters of Petilani 2:118 [A.D. 402]).
"If the very order of episcopal succession is to be considered, how much more surely, truly, and safely do we number them from Peter himself, to whom, as to one representing the whole Church, the Lord said, ‘Upon this rock I will build my Church’ . . . [Matt. 16:18]. Peter was succeeded by Linus, Linus by Clement, Clement by Anacletus, Anacletus by Evaristus . . . " (Letters 53:1:2 [A.D. 412]).