Some people assert that the Catholic Church was not started til the fourth century. They never in my experience will provide any evidence, some however will point to Constantine and the Council of Nicea.
However, the fact is we have the list of the Bishops of Rome (popes as they are more commonly called now) going back to the time of St Peter in Rome, in fact many of the major Sees are able to list their Apostolic lineage, such as the See of Alexandria can show their list going back to St Mark.
Some assert Constantine made Trinitarianism the doctrine of the Church, which is not true. Constantine himself may have been Arian. Though he did help the Church gather together for the Council of Nicea which condemned Arianism (the doctrine that denies Jesus is God Almighty), Constantine's own son was an Arian, and Constantine was baptized on his death bed by an Arian bishop, Eusebius of Nicomedia. Constantine also wrote letters expressing how the controversy was some thing "small."
Trinitarianism was taught before Nicea and the 4th century. In fact the precursor to Arianism was condemned, which was the heresy of Paul of Samosata about 5 decades prior to Nicea was convened.