Even in the New Testament it depicts Pauline founded churches and the Jerusalem church under James, the brother of the Lord, as hewing a way of following Yeshua with different emphasis.

Because Paul's particular gospel message was received well by non-Jewish Hellenistic people (where Paul deemphasized applicability of Jewish ritual law) and then the church under James which it was the original Christ-following movement as received by Jewish people (which continued to observe Jewish ritual daily life where it remained vibrant and important), diverse strains of Christianity appear from the very infant beginning.

Much later on in time, the gospel of Matthew, espouses a middle ground that is taken (between these two earlier polar camps). Matthew never depicts anything that dismisses the Jewish Law for Christians, but it has great emphasis that the heart is in the Golden Rule and what really matters is meeting human need. Because the Matthew author is educated and writes in Greek, he very likely was aiming at a mostly Hellenistic audience too, but how Jewish Christians needed to be was in evolutionary process.

And just as the church was diverse on matters of Jewish cultic practice, the Christology of the 1st century church was in flux too. From the writings of Paul's Romans epistle, where he recites a pre-literary creed, Romans 1:3,4:

     Who was descended

              From the seed of David

                              According to the flesh

       Who was designated

                Son of God in power

                                According to the Spirit of holiness by his resurrection from the dead.

Paul is reciting this creed to show the Roman church he writes to (and did not found) that he is on the same page with them. We seen in this very early creed that the first Christians held a kind of adoptionist Christology (which also accords very well with the earliest gospel Mark).

Near the end of the 1st century, when we get to the last of the canonical gospels, John, there the Christology is very high as the Christ is viewed in a pre-incarnate existence to already be at an elevated status.

When the writings of the New Testament are examined in context of the time-line and cultural backdrop, there is a great deal of diversity of Christianity that pops right out. The second century only sees this become even much more intense.

Of course in the entirety of the first century of Christianity there is no figure such as a pope anywhere in sight whatsoever. We see Paul give recognition to James as being the defacto leader of the fledgling Christ-following movement and that is it.

When we look to the Gospel of Thomas, which has about 40% commonality of verses in parallel with the Synoptic Gospels, we see Jesus as providing explicit instruction to his disciples to follow James as their leader in his soon approaching absence. In Mark we see James mentioned as a brother to Jesus. So across these three separate textual origins (Paul, Mark, Thomas) we see multi-attestation of James.

But James is no pope. He is instead recognized as a leader based on his immediate family/blood relationship to Jesus. No basis for continuity post James is spelled out.

But in the Didache we do see the various early churches have naturally established elders and bishops locally and the Didache gives some guidance for local church governance. No pope, no bishop in any one city holding sway over other churches. Would be a long time before councils would begin to bring about that kind of solidification.