One of the most important events in the early church was the First Council of Nicaea. We might think that with such an important council that the Pope would be giving leadership to it. But in fact, the Pope did not attend the council.
What we need to remember is that the bishop of Rome was not known as the Pope at that time, nor did that bishop have the same authority over other churches and bishops the way we know it now.
The bishop of Rome at the time was Sylvester I (285-335 AD). Sylvester did not attend the council but did send representatives and did approve of the decisions made at the council.
Why did the bishop of Rome not attend?
While the church was not officially split between the west and the east as it would eventually be, the Empire did have a west and and an east. There were various differences between the two halves, including culture and language.
This also included theology to a certain extent. The Arian controversy was seen as an eastern issue and one that it was not as relevant to the west. Not only that, the council was in the east, in Nicaea in modern day Turkey. It was not as convenient for western bishops to attend and the east was much better represented.
We do not know a lot about Sylvester I and in some ways we know less about him than we used to know. There were many legends about Sylvester I, much of that based on later forgeries. This included the Donation of Constantine that came up with a fictional agreement between Sylvester I and Constantine the Great. Once the forgeries have been peeled away, we are left with very little information about the historical bishop of Rome.
The claim that the bishop of Rome was not or was not seen as the head of other bishops is utterly false.
There is absolutely no historical basis for claiming that Peter (the apostle) was the first Pope. No such mention has been made by the well-known church historians of that time (or since). The Catholic Church retroactively appointed Peter as the first Pope, but the title (Pope) and associated title (Vicar) did not yet exist. Was Peter instrumental in establishing the church in Rome? Most assuredly, he was. Did he help to prevent an early church schism between those who advocated that Gentiles must abide by Jewish dietary laws and circumcision versus those who disagreed? Most assuredly, he did. The Catholic Church loses credibility by insisting on false claims about Peter as the 1st Pope.