The Catholic teaching — as well as historical fact — is that the deposit of Faith was delivered to the Holy Apostles prior to the books of the New Testament were written. St Jude speaks of it: “concerning your common salvation, [...] contend earnestly for the faith once delivered to the saints” (Jude 1:3).
The Apostles initially taught orally, resorting to teaching by letter when they could not meet the audience face to face, and in 2 Thess. 2:14 plainly says that the tradition that he teaches has the same weight as the written word. Obviously, we are not talking of customs and ceremonial culture here but of the historical, apostolic method of interpreting the scripture, prayers, hymnody and iconography that together with the Scripture shape our faith since the times of the Early Church.
Keeping in mind that the only Scriptures that existed at the time were the Jewish Scriptures that Jesus taught.