Peter was not, according to some evidence, the first Pope.
The earliest accounts mention the fact that Rome’s Christian community was founded by Sts. Peter and Paul. Irenaeus wrote that Peter was not acting alone… “Matthew also issued a written Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching at Rome, and laying the foundations of the Church.”
Ireneaus goes on to say
“Since, however, it would be very tedious, in such a volume as this, to reckon up the successions of all the Churches, we do put to confusion all those who, in whatever manner, whether by an evil self-pleasing, by vainglory, or by blindness and perverse opinion, assemble in unauthorized meetings; [we do this, I say, ] by indicating that tradition derived from the apostles, of the very great, the very ancient, and universally known Church founded and organized at Rome by the two most glorious apostles, Peter and Paul; as also [by pointing out] the faith preached to men, which comes down to our time by means of the successions of the bishops. For it is a matter of necessity that every Church should agree with this Church, on account of its pre- eminent authority, that is, the faithful everywhere, inasmuch as the apostolical tradition has been preserved continuously by those [faithful men] who exist everywhere. The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate.”
Eusebius also accepts this role for Linus "The blessed apostles having founded and established the church, entrusted the office of the episcopate to Linus. Paul speaks of this Linus in his Epistles to Timothy.
In the west the idea of Petrine supremacy would rise, and accordingly later writers would tend to stress the role of St. Peter in Rome’s foundations, but the earlier writers were not burdened by such dogma. Reading Irenaus further we see that he doesn’t count a bishops line from St. Peter at all, but from Linus…“Of this Linus, Paul makes mention in the Epistles to Timothy. To him succeeded Anacletus; and after him, in the third place from the apostles, Clement was allotted the bishopric.” What also is important to note again is the repeating of the idea that Linus’ tenure came after and upon the foundation of all the Apostles, plural.
Many people accept the idea that Peter was the first Pope. Some early sources state that St. Peter did not even ordain Linus as the first Bishop of Rome!
“Of the church of Rome, Linus the son of Claudia was the first, ordained by Paul; and Clemens (Clement), after Linus’ death, the second, ordained by me Peter."
 Irenaus, “Against Heresies”, Book III.1.1 (quoted at ccel.org/fathers2/ANF-01/anf01-60.htm#P7297_1937859)
 Ibid. Book III.3.2-3
 Eusebius “The History of the Church” Book V Chapter VI. Catalogue of the Bishops of Rome cited at ccel.org/fathers2/NPNF2-01/Npnf2-01-10.htm#P2930_1381485
 Irenaus. Book III.3.3
 “Apostolic Teaching and Constitutions,” Book 7, Chapter XLVI – “Who Were They that the Holy Apostles Sent and Ordained?” quoted at