You say they “claim” there would be no Bible were it not for the Catholic Church. Why would you use the word “claim” as if there some doubt as to where the Bible came from?
Interesting question.
It seems that a major part of the 'bible' was already in existence - what we now call the Old Testement.
And what's now in the New was FOUGHT over (by Catholics) as to which writings would be included or tossed.
To say that ONLY the Roman church would have collected and assembled the NT is, by definition, boastful and arrogant.
Much like the whine of the OT prophet who was convinced that ONLY he was left to carry on GOD's work.
He soon found out; from GOD; that there were a VAST number (7,000 I think) of His followers around that Jezebel was NOT trying to kill!