The New Testament is clear: the early Church was governed by the apostles who were hand-selected by Jesus himself. But what happened after the apostles died?

For both Matt Swaim and Ken Hensley as Evangelical Christians, their general assumption was that once the last apostle died, it was as though a switch flipped, and the whole of Christianity shifted to a view that Scripture alone was the sole and sufficient rule of faith.

But does the testimony of the New Testament give any indication that Peter, John, Paul and the other apostles were setting up the Church to be governed by the doctrine of sola Scriptura after their deaths? Or is there another understanding of authority, found not only in the pages of Scripture, but also the historical record of early Christianity, that better explains how the apostles intended their successors to operate?