Clement of Rome says the apostles appointed bishops and deacons and provided for approved successors (1 Clement 42–44). Ignatius repeatedly addresses the bishop, presbytery, and deacons as distinct ministers around whom the local church gathers. Justin describes a president offering the Eucharistic thanksgiving and deacons distributing the gifts (First Apology 65–67). Later ordination rites and canons make the laying on of hands and authorization still more explicit.
The earliest vocabulary is not mechanically identical in every source, and scholars debate when the monoepiscopal pattern became universal. That caution does not rescue the claim that any believer could simply assume liturgical presidency at will. The surviving record knows ordered, appointed ministry from the Church’s earliest post-apostolic generations.
Primary sources
1 Clement 42–44: https://www.newadvent.org/fathers/1010.htm
Ignatius, Smyrnaeans 8: https://www.newadvent.org/fathers/0109.htm
Justin, First Apology 65–67: https://www.newadvent.org/fathers/0126.htm