Joseph was skilled but he was still a laborer. The term "lower middle class" is completely anachronistic, but something like that is probably close to the right idea. Their household undoubtedly had many needs with extended family around, but they doubtless could not afford servants. And we know kids from working class families are always less likely to have time for school, especially before modern times. (And in this case, before 70 AD.)
What about rich kids? Some Nazarenes must have been landlords or landowners, or at least local property managers. Wealth being relative, Nazareth no doubt had some Jews who were richer than others. We may also note that Jesus spent a lot of time talking about wealth and the wealthy during his public ministry. The odds are therefore fairly high that he knew rich folks during his three decades in Nazareth. (To be fair, Jesus probably visited Sepphoris from time to time, which had more money, and was probably home to some villages' absentee property owners.)
If Nazareth had some rich folks then they probably had some education. The more wealthy Synagogue members in town, the more likely it is that their Synagogue hired (full or part time) a children's tutor for the betterment of their whole community. In later antiquity, children's training was typically held in the mornings, and sometimes perhaps for adults in the evenings. In Jesus' day, we can only guess whether Nazareth had such a tutor on staff, but a local Rabbi could also have volunteered time when he was able. These are both definite possibilities.
Now, even though we may find it likely that the Synagogue probably did offer some teaching sessions, we still don't know whether Jesus was able to attend any of them. However, we should expect that a carpenter's son was unlikely to make all of them. Some of us may want to suppose Joseph made special provisions so that he could, but it may be more likely that Jesus attended when work days were slow. However, again, we are not trying to speculate. These are simply the potential options. At the moment, we are only trying to narrow things down.
Beyond regular 'school', it is very likely that visiting Pharisees would give lessons when they were in town. If there were no children learning, there would be no future disciples to train up as future Rabbis (who visiting Pharisees naturally hoped would side with the Pharisee party). It is true that the Sanhedrin did not expect Prophets to come out of Galilee - or probably anyone else of educational consequence - but the Pharisees were far more bound to the common folk than the dominant Sadducee Party of Annas & Caiaphas. Besides, any good recruiter hits even the coldest spots once in a while, and Jerusalemites had been developing Galilean Judaism for a hundred years when little Jesus was first brought to Nazareth. All things considered, some traveling Law teachers must have come through at some times. However often it happened, these were more opportunities for Him to hear scripture read out loud at the Synagogue, and (less often) to see and to hold it.
In all this, we should emphasize that we still have no precise idea about what went on mid-week at the Nazareth Synagogue. We cannot reasonably estimate how many regular or special opportunities Jesus had in his upbringing and later life to enhance the educational input he was receiving on Sabbath days. However, we should think there were some. The high probability of some such opportunities is something we definitely should keep in mind, even though we have no reason, as of yet, to say whether the Lord actually took advantage of any of them.
In the end, his only Synagogue lessons may have come on Saturdays. Soon, therefore, we must ask the question - could Sabbaths alone have given Jesus enough input to account for whatever he meant when he said, "My teaching is not mine, but his who sent me?" Naturally, in keeping with the rest of this series, we will attempt to answer this question with direct evidence from the Gospels, and not with interpretative theo-logic.
But before we finish our considerations about educational opportunity, we need to focus for one brief post on educational resources. To the best of our knowledge, what scrolls were actually kept in the Nazareth Synagogue? And were there other copies of scripture, around town?
To be continued...
Series Update: The Nazareth Synagogue