When did the Roman catholic religion began?

The term "Roman" in "Roman Catholic" is to designate the Roman-Rite, the 'Western' Rite" of the Catholic Church. There are other "rites" in the 'Uniate' Churches, ie: Ukranian Catholic...

the "catholic" Christian Church began at the time of Christ. The term "Roman" "Ukranian" etc. came into use at the time of the Reformation to define the different denominations within the splintered faith.

-Roman Catholic Church was founded in 33 AD, though we had yet to get the name.