Well, as far as apostolic succession goes it is linked to the last of the attributes of the Church mentioned in the Creed; specifically, that the Church is apostolic.
IV. THE CHURCH IS APOSTOLIC
857 The Church is apostolic because she is founded on the apostles, in three ways:
- she was and remains built on "the foundation of the Apostles,"
362 The witnesses chosen and sent on mission by Christ himself;
363
- with the help of the Spirit dwelling in her, the Church keeps and hands on the teaching,
364 The "good deposit," the salutary words she has heard from the apostles;
365
- she continues to be taught, sanctified, and guided by the apostles until Christ's return, through their successors in pastoral office: the college of bishops, "assisted by priests, in union with the successor of Peter, the Church's supreme pastor":
366
You are the eternal Shepherd
who never leaves his flock untended.
Through the apostles you watch over us and protect us always.
You made them shepherds of the flock
to share in the work of your Son....
367
...
The apostolate
863 The whole Church is apostolic, in that she remains, through the successors of St. Peter and the other apostles, in communion of faith and life with her origin: and in that she is "sent out" into the whole world. All members of the Church share in this mission, though in various ways. "The Christian vocation is, of its nature, a vocation to the apostolate as well." Indeed, we call an apostolate "every activity of the Mystical Body" that aims "to spread the Kingdom of Christ over all the earth."
377
864 "Christ, sent by the Father, is the source of the Church's whole apostolate"; thus the fruitfulness of apostolate for ordained ministers as well as for lay people clearly depends on their vital union with Christ.
378 In keeping with their vocations, the demands of the times and the various gifts of the Holy Spirit, the apostolate assumes the most varied forms. But charity, drawn from the Eucharist above all, is always "as it were, the soul of the whole apostolate."
379
865 The Church is ultimately one, holy, catholic, and apostolic in her deepest and ultimate identity, because it is in her that "the Kingdom of heaven," the "Reign of God,"
380 already exists and will be fulfilled at the end of time. the kingdom has come in the person of Christ and grows mysteriously in the hearts of those incorporated into him, until its full eschatological manifestation. Then all those he has redeemed and made "holy and blameless before him in love,"
381 will be gathered together as the one People of God, the
"Bride of the Lamb,"
382 "the holy city Jerusalem coming down out of heaven from God, having the glory of God."
383 For "the wall of the city had twelve foundations, and on them the twelve names of the twelve apostles of the Lamb."
384
So, as can be seen from these sections in the Catechism of the Catholic Church, the Catholic Church has
always depended on apostolic succession as fundamental to the meaning of the Church, just as she as
always depended on Unity, Holiness, and Catholicity. Do you doubt these too?
In the liturgy of the Eucharist we are taught to pray
In communion with those whose memory we venerate,
especially the glorious ever-Virgin Mary,
Mother of our God and Lord, Jesus Christ,
and blessed Joseph, her Spouse,
your blessed Apostles and Martyrs,
Peter and Paul, Andrew, [Apostles in Rome]
(James, John,
Thomas, James, Philip,
Bartholomew, Matthew,
Simon and Jude;
Linus, Cletus, Clement, Sixtus, [the first popes in Rome after saint Peter.]
Cornelius, Cyprian,
Lawrence, Chrysogonus,
John and Paul,
Cosmas and Damian)
and all your Saints;
we ask that through their merits and prayers,
in all things we may be defended
by your protecting help.
This is part of the Canon of the Mass, the most ancient part of the text of the mass, It has been suggested that the present Canon was a compromise between the older Greek
Anaphoras and variable Latin Eucharistic prayers formerly used in Rome, and that it was ordered in the fourth century, possibly by
Pope Damasus I (366–84).
So, it seems that the first several popes in the current list of popes goes back to the fourth century at least.A