the body of believers, the church does predate the writing of the books of the New Testament, yes. You are correct that this body of Christ does not predate the writings of Genesis, but the body of all believers (our Jewish brethren) go back to Adam.
And yes, the canon was finalized in council. It is not just a burning in the bosom moment :), but grace from God given to His community, the church (not just the hierarchy) to compile the canon.
But not the Bible, as I've had to make clear to more than one catholic.
There are the uneducated in all denominations, catholic included.
Some of these don't understand that God was alive and active and even inspiring scripture far before the Pope came on the scene.