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As I said earlier, I'm not a defender of Luther's doctrine. The reason for not being so is that so often is left out of that equation is the functioning of God's spirit in leading us to understanding of His will. Perhaps I'll call it SSS, Sola Scriptura plus Spirit.

That may be the view of Sola Scriptura advocates but I don't hear the connection often if at all.

“How could Luther’s doctrine have been begun by Jesus in His earthly ministry?”

The reliance on the written word of God as THE guide is evident in the command given in the Law for the king to have his own copy of the Law.....and to read it just as the common male was required to read it.

When Daniel had a question about prophecy he consulted the written word of God, the writings of Jeremiah. (Dan. 9:2) and referred to “the written law of Moses”. (Dan. 9:13)

Thus Jesus took the scroll of Isaiah and read from it he defended himself against Satan by saying “it is written”.

That reliance on the written word of God is evident long before Jesus’ ministry and continued long after, no qualifiers needed.

“The early Church taught authoritatively by letter AND by word of mouth, as St. Paul writes”

Word of mouth indeed as few could own their own scrolls. But that word of mouth was subject to verification by written Scripture or testimony from one of the apostles as the Bereans did.

The Canon of the Bible was completed by the end of the first century with John's writings. What was left was the recognition of those books that were not so widely distributed or popular but that came in time.
Therein lies the leading God's spirit as many fraudulent books came into existence, imitating but never matching the genuine, were weeded out.

Not even angel could declare a “good news” contra to what the apostles has written and taught. (Gal.1:6-9)

Yes, to the topic of the thread:
Jesus foretold the present state of affairs as it pertains to his church in the parable of wheat and tares. And that the two would grow to maturity, indistinguishable until then and the harvest time. (Matt. 13:24-30)

How do you recognize that visible church?