The Church is the Body of Christ and is inseparable from faith. That’s what happened on the day of Pentecost. The Church started. And Jesus said the Peter was the rock on which it would be built.
And yes, the Catholic and Orthodox Churches trace their beginnings to the first century in an unbroken line.
Saw today what looked like a large number of Eastern Orthodox as well as Eastern Rite Catholic leaders during the service/mass.
Jesus did not say Peter was the “rock”. Peter was the small rock, but on the big rock of the statement that “You are the Messiah, the Son of God.” the gathering of Jesus was built. Go read the Greek. The Roman myth has brainwashed millions.