A bit simplistic and not at all logical: many of the first Christians were also Jews and as such, they had..........The Tenach which included all the 5 books of the Law (the 5 books of Moses), the Prophets, major and minor and the writings.
They were taught from early childhood as The Law proscribes so they were not ignorant of God. Even the Greeks who lived around the Jewish communities, knew some of the Jewish writings and many also attended the synagogue.
Waiting for the "New Testament" didn't take long for Mark wrote the story of Christ 30 years after his death, as Mark was a young teen when Christ died, so the learned believe.
The Bible is God's auto-biography and if one want's to know God, to know about God, reading God's inspired auto-biography would be paramount.
So you figure the Bible is needed to be saved? Or to have a relationship with Christ? I don’t think you do. You say “many” had the Tenach. I doubt it. It would be a big deal to copy the Tenach by hand.