No, believing Jews wrote the New Testament.
St, Paul's faith, for example, was a faith which was a continuation of the Old Testament which along with the New Testament was written by the Holy Spirit. Paul understood that the Old Testament promises to the Jews had been fulfilled in Christ. Both Old and New Testament saints were combined into one party of believers.
Old Testament believers were not Catholics either yet they were able to both interpret and explain Scripture to their hearers.
I wonder how many generations it took for this proto-church to decide it was “the one true church” and start the process of evolving into what we call the Catholic Church today?
It would be a very interesting history project, especially since a lot of history has been so rewritten.