Where was Jesus, and what did he do in the years prior to the beginning of his ministry as told in the gospels?
As far I know, the Gospels do not tel anything concerning the midle years. Actually a Gospel is the testimony of the words and facts of Jesus from the baptism until the ascencion. The four Gospels respect that "rule", even the gospel of Paul.
Matthew, Luke and Jhon originaly contained only the Gospel; that is from baptism until ascencion. Later; probably to stop the false gospels of the baby and young Jesus; they (Matthew, Luken and Jhon) included few word about the birth of Jesus.
If somebody takes Jesus as a character, as an hero of a tale; the natural tendency is to imagine his childhood. That hapens to almos all characters from Hercules to Superman. Even your curiosity to know about a young Jesus abeys to that natural tendency.
Your curiosity is normal. I did have it in my first years as christian. It is possible to asume that Jesus lived the "middle years" at Nazaret. We can asume that he worked as carpenter or constructor (the greek word for carpenter and constructor is the same) with his father. I understand that Mary and Joseph had some children after Jesus birth. You can found the names on the Gospel. Eventually Joseph died in an uncertain year. Probably Jesus becomes head of the family. We can asume that Jesus continues to searchr in the scriptures about the Christ (Messiha). Many christians believe that Jesus had conection with the escenians (i dont know the correct name in inglish).
I have read about the essenes. Apparently there is some evidence/speculation that Jesus spent some time in their dessert community. Jesus' affinity towards this sect might explain his criticism of the Pharisees and Saducees in the New Testament, as the Essenes rejected much of their interpretation of the Laws and the Torah.
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I also think we can assume that Joseph was no longer living at the time of the wedding in Cana, as there is no mention of anyone but Jesus' mother at this time. Also, Jesus makes a request to John on the cross to look after his mother after his death. I don't think he would have done this had his father been around.