“I tell you that you are Peter, and on this rock I will build my church”. (Matthew 16:18)
Though it is likely that Peter did spend some time in Rome in later life (cf. 1 Peter 5:13) and probably died there in the persecutions instigated by Nero, the tradition that Peter was the first bishop of Rome is quite late in origin. Even if he had presided as elder in the church at Rome prior to his death, there is no evidence that he commenced a succession of Popes. It is also important to bear in mind that at this point in history the church at Rome was probably quite small compared with the Christian communities in Jerusalem and Antioch.
Looking at the account of Acts 15 is quite informative: the council was held in Jerusalem, and although both Peter and Paul spoke at the council, it is James who has the final word and appears to be the chief elder there.
Matthew 16:18 is not talking about the foundation of an apostolic succession or a church hierarchy. Most likely Jesus is referring to the leadership of Peter of the community in Jerusalem shortly after Jesus’ ascension.