Church offices are different than church employees.
Are you admitting that Archbishops are not Biblical Church offices ordained by God and have no authority over actual office holders?
Cardinals are not among those Biblical essentials. You could have church without Cardinals. They are essentially bishops who hold titular churches in Rome, so they can participate in papal elections. Similar to the Pope, who is essentially the Bishop of Rome.
But actually, popes could be chosen by drawing straws or throwing dice, i.e. casting lots.
Now there's an interesting thing: that is a solidly Biblical way to make a decision, and my church doesn't do it! Does yours?
Choosing King Saul: See 1 Sam. 10:20-24. (And although less obvious, see also 1 Sam. 16:7-12 about David).
Making Difficult Decision: "Casting lots causes contentions to cease, and keeps the mighty apart." Prov. 18:18
Priest’s Order of Service: "Thus they were divided by lot, one group as another, for there were officials of the sanctuary and officials of the house of God..." 1 Chron. 24:5-19. Thus priestly families who lived in the Galilee did not have to argue about who would have to travel to Jerusalem in the cold of winter or in the heat of summer. And 1,000 years later, the priests were still casting lots, for...
Zacharias in the Temple: "according to the custom of the priesthood, his lot fell to burn incense when he went into the temple of the Lord." Luke 1:9
Making Governmental Decisions: After the rebuilding of the wall, to repopulate their capital city, the Israelites “cast lots to bring one out of ten to dwell in Jerusalem…” Neh. 11:1
To Establish Apostolic Succession: "And they cast their lots, and the lot fell on Matthias. And he was numbered with the eleven apostles." Acts 1:26. This is how God's chosen leadership group was provided with successors. A key moment in the history of the Catholic Church: apostolic succession.
And on and on. Lots of Biblical examples. But most churches don't cast lots these days.
And some don't even have Apostolic Succession.
THe ones that do, though, have an unbroken link of authority going back to the NT, and conveyed by another Biblical action: the laying of hands.
Writing about AD 94, Clement of Rome states that the apostles appointed successors to continue their work where they had planted churches and for these in their turn to do the same because they foresaw the risk of discord. He uses both ‘bishop’ and ‘presbyter’ to refer to these men. He supports an approved continuation of the apostolic ministry which in its turn was derived from Christ. And Clement wrote this before the death of the last Apostle.