"There were no Catholics until the Council of Nicea in 325 AD."
This is incorrect.
When Eusebius, Bishop of Caesaria, wrote his History of the Church in the 290s AD, and subsequently updated it, he wrote about the Catholic Church, by that name, and he cited documents from much earlier times that, similarly were Catholic or called themselves Catholic.
There has been a Catholic Church, consciously aware of itself as such, since the days of the Apostles, and there have been bishops of said church self-consciously CALLING IT THAT in documents dating from before 100 AD.
So, while it is not historically inaccurate to assert that there were other competing Christian sects from the earliest time, it is simply wrong to argue that there was no Catholic Church before the Council of Nicaea.
Eusebius wrote a comprehensive history of the Catholic Church a quarter of a century before Nicaea, and he traced the lines of various bishops and patriarchs back. The 100's AD is ancient to us, but it was almost within living memory of the men of Eusebius' age. Now, they very well may have argued as to the authenticity of doctrines, but one thing they WEREN'T arguing about (we have libraries of their documents) was whether or not the Catholic Church EXISTED. OF COURSE it existed, with its bishops and priests and deacons and deaconesses, hermits, etc., just as it already did when Paul writes his letter to Timothy explaining the proper procedures for selecting a bishop. Notice that Paul makes no attempt to describe what a bishop IS. Everybody who was going to receive any of his letters already knew THAT. Paul was writing to a Church that was already Catholic. Doctrinally in ferment, perhaps, but already organized on lines familiar to us. Which is why there's no formal Constitution of the Church in the New Testament. Paul tells his readers who should be bishops and priests and deacons and deaconesses. He talks about The Lord's Table without explaining what it is. Etc. He didn't HAVE to, because he was writing to people who already knew what a bishop was, and a priest and deacon, and what the Lord's Table was, etc. Because they were already Catholic.