In fact, it's later than that.
I agree with ealier proposed dates on the gospel dating myself. But even with these you're talking about the synoptics being dated around the 60's - possibly the 50's - and John somewhat later.
Revelation (the Apocalypse) of course wasn't written until later (80's or 90's). The eastern church didn't accept it until about 400 A.D.
So the first two to three generations grew up in the faith without any - or very much - written scripture, and certainly no canon as such. One wonders what the sola scripture folks make of that.
In the meantime they had the faith as transmitted by the Apostles and their appointed successors - the first presbyters (priests) and bishops. And it was those priests and bishops, in the form of the Church, that compiled and established the canon.
On the contrary...the scriptures were being handed around. They just hadn't been compiled into a book until the heretic Marcion made this necessary.