The early church was born out of the apostolic tradition that was given from Christ Himself. What the apostles received they passed on to the church and “other learned men”. Before there were New Testament scriptures there was only apostolic tradition. Years later, the Gospels and the Epistles were written based on that apostolic tradition. Then centuries later, those writings that were inspired were discerned by the church, guided by the Holy Spirit, and compiled into what we eventually would come to know as the New Testament.
Those in the early church did not wait until inspired writings had come about to act on the teachings of Christ. They followed the tradition that was given to them. When writings did come about they did not forsake the tradition, but considered scripture and tradition to be on equal ground, complimenting each other, and originating from the Holy Spirit.
This adherence to tradition is exactly what Paul commends the Corinthians for doing,
1 COR 11:2Now I praise you, brethren, that you remember me in all things and keep the traditions just as I delivered them to you.
This commendation by Paul makes no distinction between the written scriptures and oral tradition. It is one and the same. It is the combination of the two, that is to be considered the Word of God, and this is what the church is founded on.
The book of Acts spends a lot of time showing what the apostles did. Starting churches, going to churches, going to synagogues, going to public squares. While they did write during this time, not nearly as much time was spent on writing as proclaiming the Word of God. Passing on the Tradition they had received.
In Acts we read of the Bereans, who search the scriptures daily,
ACTS 17:11These were more fair-minded than those in Thessalonica, in that they received the word with all readiness, and searched the Scriptures daily to find out whether these things were so.
What is that the Bereans received? It couldn’t be the Old Testament, because they already had that. What was received was tradition and they checked what was received by the Old Testament scriptures. The Old Testament was used as a witness to Tradition, not a replacement.