Please do link/quote at least some of the many answers to that question. I’m new here. Perhaps I’ve missed them.
My guess is that none of the answers actually answer the question, but please do prove me wrong.
Some portions of what should be wider answer have appeared on this thread. Did you miss those?
Other, wider explanatory "answers" have and do address the question...but do not as they cannot, fully set aside "tradition". Yet with the NT, those works came to be all but self-selecting, in that most all of them enjoyed wide circulation and acceptance from quite early on.
Here's the deal;
What do we see now but NT canon restricted to those sources actually Apostolic? One can ask "what about about Luke, and the book of Acts?" but Luke obviously was well entrenched within the community itself (he received first person testimony from many) and as for the Gospel of Luke itself, Paul in one of his Epistles cites a passage from Luke right as he is also citing and referring to "scripture". Nowhere does Paul attempt to refute or correct the Gospel of Luke that I am aware of. No one else successfully did either...right?
What's left BUT that which is in actuality from Apostles themselves, or those closely with them from the beginnings? That is the "self-selective" aspect.
I've seen other writings attributed to Peter, and read through them, wondering why they lacked in power, before discovering those most likely were not from the Apostle Peter, but were merely presented as being so. There WAS a bit of that sort of thing going on from very close to the beginnings of the church, but were fairly well weeded out before later, "formal" church councils discussed issue of canon, though I do admit it is not a story without some complexity, due much to pseudographical works trying to pass themselves off as 'Apostolic'. along with some NT "apocrypha' which though possibly helpful in some respects, was not fully accepted as being on the same level of inspiration, much less directly Apostolic, thus authoritative. Reading those today, one need be but familiar with that which is NT canon to see the differences. Those same "differences" of course existed in comparison of texts-to-texts then, as they still do.
Here, try this The Formation of the New Testament Canon Steven Voorwinde, Professor of New Testament at Reformed Theological College, Australia
His analysis beats the pants off of most argument seeming designed to use the history of formation of NT canon as leverage towards declaration that even now, in this day and age, the only "authority" possible be that of Rome's self-proclaimed own.
Voorwinde doesn't come across as being polemical (as is my own above 'editorial comment').
Voorwinde arrives where he does through scholarship, providing footnote and documentation for his work as he goes along, with his own scholarly presentation much refuting where some seem to be trying to push Romanist positional argument, rather by default than by design.
That said...this single sample of 'source' (the link provided) along with other documentation, much of them Voorwinde lists as footnote, have been quoted from, linked to, discussed (dismissed out-of-hand by many a [Roman] Catholic I might add) again and again. It get's old.
The trail of bread crumbs doesn't much lead to Rome, anyway. Some of the various "trails" meander through, in regard to some Ante-Nicene notables(?) but the greater balance of such persons and 'source' of written record does not. Nor were the various churches of those days subject to Rome in any particular fashion. The papacy as we know it today...had not yet 'developed', etc.