I quote again from the Catholic Encyclopedia regarding the person James the Lesser aka James the Just. Some Catholic interpreters say he was an apostle and therefore present at the first Pentecost following the ascension of Jesus. It cannot be proven of course no matter how many early Christian writings are quoted.
“The identity of the Apostle James (2), the son of Alpheus and James (3), the brother of the Lord and Bishop of the Church of Jerusalem (Acts 15, 21), although contested by many critics and, perhaps, not quite beyond doubt, is at least most highly probable, and by far the greater number of Catholic interpreters is considered as certain (see BRETHREN OF THE LORD, where the chief argument, taken from Galatians 1:19, in favour of the Apostleship of St. James the brother of the Lord, is to be found).”
Having read Galatians 1:19 myself my personal opinion is Paul certainly considered “James the brother of the Lord” an apostle. However the commentary in the New American Bible (Catholic Translation) states this James “was not one of the twelve…he played an important role in the Jerusalem Church, the leadership of which he took over from Peter (Acts 12, 17).”
So the founding of the “Catholic” church was at Pentecost. Catholic meaning universal. The Church of Jerusalem with its subsequent line of bishops did pre-date the Church in Rome.