The First Ecumenical Council was not about uniting the RCC. It was about reducing divisions between the Apostolic Sees—Rome (the RCC), Constantinople, Alexandria, Antioch, and Jerusalem. Except for the Roman Catholic Church, the others on that list are Orthodox churches, which are autocephalous, and thus have their own popes that are separate and distinct from the Catholic pope. More to the point, although they were part of the Roman Empire at the time, they were not part of the Roman Catholic Church, and to the best of my knowledge, with the exception of one branch of the Church of Alexandria that joined the RCC in 1442 (a thousand years after Constantine), none of those other churches have joined with the RCC in the nearly two thousand years since.
More to the point, out of the two or three hundred bishops at that council, as I understand it, only about five were from the Latin rite (Roman Catholic) Church. That council had a far more significant impact on the Orthodox churches than the RCC. Its main achievement was disavowing the teachings of Arius (from the Alexandria Church, not the RCC).
Further, even if you were correct, the first Roman Catholic Pope was still the pope of the Roman Catholic Church hundreds of years before Constantine was even born, which means it clearly was, in fact, founded long before Constantine. Certainly, Constantine strengthened the Roman Catholic Church—particularly by recognizing it as a legal religion—but he most certainly did not found it, and any suggestion to the contrary is utterly absurd.
To put it another way, saying that Constantine founded the RCC is roughly like saying that FDR, by uniting the country with other nations against a common enemy, founded the United States of America.