The Church, birthed by the Holy Spirit on Pentecost, existed, grew before, during and after the New Testament was written and the books of the Bible determined.
Well, exactly. The Church comes from Christ, not from scripture. Scripture is indeed inerrant, but it gains its inerrancy from the Church.
The Church received its authority 'to bind and loose' from Christ - and one function of that authority is to define which scripture is good and inspired, and which scipture is not.
This is why we don't believe 'scripture' about Christ baking His friends in an oven, but we do believe scripture about Him giving us His Body and Blood. The Apostles chose one scripture and rejected the other, and they did so with the authority of Christ.
It is completely evident that their authority must predate and preempt scripture. Because they ratified that same scripture - and in some cases even wrote it.
The authority of the Church truly does not rest upon scripture. It rests upon the action of the Trinity: upon Christ and His words and deeds, and upon the mysterious action of the Holy Spirit since Pentecost.
Sounds like a circular argument to me. If the scriptures are inerrant, why would the scriptures need to "gain" its inerrancy?
The early church fathers knew what was inerrant and what wasn't. They didn't "approve" scripture for inerrancy. Instead they "confirmed" them to be inerrant. The early church fathers constantly talk about "receiving" the writings from God; not some approval process.