The witness of the manuscripts

There are different lines of evidence for the canon. External evidence includes Jewish testimony, the church fathers, the Muratorian canon. 

There's extensive internal evidence in terms of the intertextuality of the Bible. 

Also the fact that some books of the Bible naturally comprise literary units (e.g. Pentateuch, Psalter, Luke-Acts, Pauline Epistles, John/1-3 John).

However, I'd like to highlight a neglected line of evidence. That's the very fact that we have editions of Scripture, and we can trace that process back in time. The manuscripts are evidence.

For instance, Christian scribes don't just copy individual NT books, but groups of books, like the Gospels, or the Gospels and Acts, Pauline Epistles, or Pauline epistles plus Hebrews, or general epistles. Christian scribes transmit anthologies of NT documents. Take some of the Chester Beaty papyri. 

And that's interesting because, at the time, Christian scribes were operating independently of each other. There was no central agency coordinating their activities. So that's a historical, but decentralized witness to the NT canon. Not simply that Christian scribes copied NT books, but copied collections of NT books in larger and smaller units. 

Although the external evidence is a kind of tradition, it's not an official exercise of "the Church", but many individuals who independently bear witness to the canon.