The early Christians received the Bible from The Holy Spirit, who inspired it, not from the Roman Catholic Church.
But don't listen to me. Listen to what the "OFFICIAL TEACHINGS of the Roman Catholic Church" says in regard to both the Old Testament and New Testament books of the Bible:
"These books the church holds to be sacred and canonical not because she subsequently approved them by her authority after they had been composed by unaided human skill, nor simply because they contain revelation without error, but because, being written under the inspiration of the holy Spirit, they have God as their author, and were as such committed to the church". - First Vatican Council. (emphasis added by me for clarity).
We wouldn't have the New Testament if it weren't for Christ...and the Holy Spirit who moved men to write. It is His words to us not the churches. And frankly we wouldn't have the scriptures...old or new...if it weren't for the Jews....If any deserve the credit for what we have to day from days gone by, it is the Jewish Nation who carefully transcribed and handed down the text. The new testament stands on the old testament.
All through the Old Testament we read "Messiah is coming"...the Gospels cry out..." He is Here"....Revelations tells us.."He is coming Again". The entire scriptures are all about Christ from beginning to end...not the catholic church...rather all those who looked for Him to come, who believed in Him when He was here...and those who would believe in Him in the future....and the Jews travel throughout both testaments as well.
The path of how the New Testament was transcribed and given to us is secondary to the author and finisher of our faith Christ Jesus. Frankly I am pleased that the Lord God saw to it that we have it today and it has endured way beyond anything the catholic church might have had a hand in. What is significant is that we have it and the Holy Spirit uses it as our compass thru life and our understanding of Gods will.
CATECHISM OF THE CATHOLIC CHURCH
424. "Moved by the grace of the Holy Spirit and drawn by the Father, we believe in Jesus and confess: 'You are the Christ, the Son of the living God.'[Mt 16:16 .] On the rock of this faith confessed by St. Peter, Christ built his Church.[Cf. Mt 16:18; St. Leo the Great, Sermo 4 3: PL 54,150 - 152; 51,1: PL 54, 309B; 62, 2: PL 54, 350-351; 83, 3: PL 54, 431-432.] 'To preach. . . the unsearchable riches of Christ'[Eph 3:8.]"
552. "Simon Peter holds the first place in the college of the Twelve;[Cf Mk 3:16 ; Mk 9:2; Lk 24:34 ; 1 Cor 15:5.] Jesus entrusted a unique mission to him. Through a revelation from the Father, Peter had confessed: 'You are the Christ, the Son of the living God.' Our Lord then declared to him: 'You are Peter, and on this rock I will build my Church, and the gates of Hades will not prevail against it.'[Mt 16:18 .] Christ, the 'living Stone',[1 Pet 2:4.] thus assures his Church, built on Peter, of victory over the powers of death. Because of the faith he confessed Peter will remain the unshakable rock of the Church. His mission will be to keep this faith from every lapse and to strengthen his brothers in it.[Cf. Lk 22:32 .]"
According to the CCC (Infallible-Yes?) the Church was built on the rock of the faith confessed by Peter never upon Peter himself.
Oh, and "universal" is small "c" catholic.