I
Ignatius
Guest
Pax Christi.But it is true, and in more than vestigial form. Certainly the primacy of the Roman see was recognized before the year 200 A.D., as indicated in the writings of Irenaeus and others, and as has been noted in this thread. That’s a pretty early formulation. Pope St. Victor, who died in the year 198, makes an explicit assertion of the primacy of the Roman see when settling the quartodeciman conflict.
In response to the question in the OP, this puts the Catholic Church firmly in place before the Fourth Century.