Dr. David Fiensy, retired Dean of the Graduate School of Bible and Ministry at Kentucky Christian University, author of half a dozen books on Biblical archaeology (including the excellent Christian Origins and the Ancient Economy) and participant in seven archaeological digs in the Holy Land, especially in Jesus' region of Galilee, answers that question in this short video.
According to Dr. Fiensy, skilled artisans (for instance, a 'tekton' like Jesus) were generally high in demand. There were chronic artisan shortages in the ancient Mediterranean region. This was even more true in Israel in general and in Galilee in particular. The Temple employed hundreds, maybe thousands of workers during its long construction period, which included the earthly life of Jesus.
Commentators have talked about Jesus being of the simple peasant farming community of Nazareth for at least a century. This raises some puzzles which they have been unable to satisfactorily resolve, like how could Jesus, an alleged country bumpkin, know enough about finance to tell complex financial parables? Why do His parables match so well with known business practices of the time for upper middle class merchants?
In this short video, Dr. Fiensy argues that is nearly inconceivable that Jesus lived and worked only in Nazareth. There were two major building booms in two cities quite near to Nazareth: Sepphoris and Tiberias. Sepphoris was within easy commute distance of Nazareth, an hour's walk or so. It is even reasonable to think that Jesus might have worked on the Temple itself, given that Herod aggressively south skilled workers, including carpenters. Whether Jesus worked on the Temple or not is unknown, but for Joseph & Son (or at least foster Son) builders to have survived, they would have been very unlikely to limit themselves to just the handyman tasks of a small village, especially when a major building boom was underway almost next door.