You mean the people who canonised the Bible in the first place? The Church existed long before the Bible did.
Before the collection of the NT, yes, but not before the OT, which is what Jesus used to show the gospel:
Luk 24:25 And he said to them, “O foolish ones, and slow of heart to believe all that the prophets have spoken!
Luk 24:26 Was it not necessary that the Christ should suffer these things and enter into his glory?”
Luk 24:27 And beginning with Moses and all the Prophets, he interpreted to them in all the Scriptures the things concerning himself.
...
Luk 24:44 Then he said to them, “These are my words that I spoke to you while I was still with you, that everything written about me in the Law of Moses and the Prophets and the Psalms must be fulfilled.”
Luk 24:45 Then he opened their minds to understand the Scriptures,
Luk 24:46 and said to them, “Thus it is written, that the Christ should suffer and on the third day rise from the dead,
Luk 24:47 and that repentance for the forgiveness of sins should be proclaimed in his name to all nations, beginning from Jerusalem. (ESV)
That is the gospel, given by Jesus, which Paul preached and was clearly prior to the Church. More than that, not even Paul himself, nor any other apostle, claimed what you and the CC are claiming. Rather, Paul admitted that he didn't know everything:
1Co 13:12 For now we see in a mirror dimly, but then face to face. Now I know in part; then I shall know fully, even as I have been fully known. (ESV)
Paul states that he doesn't see perfectly, that he sees as "in a mirror dimly." That would apply to Peter and the rest of the apostles, which means that none of them can be an infallible authority; it means that no person, including every Pope and Patriarch, could be, ever.
Okay. This begs the question...who is interpreting scripture?
Believers, both leaders and lay. Everyone holds everyone else accountable:
Act 17:10 The brothers immediately sent Paul and Silas away by night to Berea, and when they arrived they went into the Jewish synagogue.
Act 17:11 Now these Jews were more noble than those in Thessalonica; they received the word with all eagerness, examining the Scriptures daily to see if these things were so. (ESV)
We have a very clear example of the people holding the apostles to account for what they were preaching.