The Gospels do tell us that Jesus could quote from all of the following: all five books of Moses, some History and Psalms of David, every major Prophet and about half of the minor ones. Jesus also made claims about "all the Law and the Prophets" which may or may not imply that he'd read the entire "Old Testament" and possibly then some. We must acknowledge that Jesus visited Jerusalem and that Pharisees who visited Nazareth could carry scrolls on their journey, but it is most likely that Jesus learned all these scriptures in Nazareth, at his local Synagogue.
There is no question that all Synagogues valued the scriptures and undoubtedly desired to have at least one copy of all their traditionally sacred writings. But did they? The question boils down to three things - time, money, and manpower. To illustrate:
Individual Jews and Christians in antiquity simply did not possess personal copies of "the Bible". Even if a very wealthy person paid a group of scribes to transcribe a collection of scrolls, full time access to any (probably far away) scriptorium was not commonly available. You needed connections. Even then, the financier would still have to cover the costs for countless man-hours, expensive specialty item materials (let's not even get into that, please), access fees for time spent with the master copies, and perhaps even security for the documents' protection.
Without instigating such operations, wealth alone was not typically sufficient for such a procurement because - functional literacy being as low as it was - sacred writings were certainly not being peddled at Jewish street markets across Palestine. These economics of publishing, especially publishing of the sacred word, remained fairly consistent until the 16th century AD.
In first century Palestine, it was simply unheard of for individuals to have personal copies of the scriptures. The fact that it took so much trouble means we should actually be fairly amazed to think a small town in Galilee could afford it. But Synagogue costs were corporately defrayed, and their connections ran straight through Jerusalem. Also, the Nazarene scroll collection probably took several decades to grow, possibly subsidized by wealthy Jerusalemites who stayed involved in bringing along the "new" converts, since about 104 BC.
The Nazareth community may or may not date back that far, but it's probable because their location was good (hidden from three sides on semi-high ground with at least one natural spring, and close to good farmland and other resources). However many decades the Synagogue had been building their scroll collection before 4 BC, that expense should have been a priority, over a building. So whatever the odds that the word "Synagogue" in the gospels refers to a free standing purpose built structure, instead of merely whatever place the community held their gatherings (see post #3), such are the odds that their scroll collection was most likely complete, or at least sufficient enough by the standards of their peers to proceed.
If they had a building, they probably had a large scroll collection. If they had no building yet, they'd still had decades to build up that collection. Either way, the Gospels account of what Jesus could cite is not at all an unreasonable estimate of what Nazareth actually held in their 'library'. But we should definitely NOT imagine Jesus had his own copy of the same scriptures.
We may now return from the question of resources, to the question of how much time Jesus might have been able to spend accessing them.
To be continued...
Series Update: The Nazareth Synagogue