Did the early church believe that St. Peter was the first pope?

Roman Catholics believe that St. Peter was the first Pope, had primacy over the church and was given a pastoral role by the Lord Jesus Christ himself, we know the scripture argument for the papacy, which is Matthew 16:16-18: > And Simon Peter answered and said, Thou art the Christ, the Son of the > living God. > > And Jesus answered and said unto him, Blessed art thou, Simon Barjona: > for flesh and blood hath not revealed it unto thee, but my Father > which is in heaven. > > And I say also unto thee, That thou art Peter, and upon this rock I > will build my church; and the gates of hell shall not prevail against > it but is there any historical evidence from AD 100-200 AD that the early church held to the papacy?