Jesus could have indeed been a carpenter. This was the occupation of his earthly father, Joseph. A carpenter makes things out of wood. It was common in those days for the oldest son to be apprenticed to his father and take on the occupation of the father, so perhaps he worked for a time as a carpenter. He was 33 years old when he began his ministry, so what was he doing in the meantime? There is only one instance, when he was 12, that gives any information before he came upon the scene at age 33. In the Bible, in the book of Mark, chapter 6, verse 3, some people are questioning Jesus' right to be teaching about the Scriptures, and they ask, "Isn't this the carpenter's son?"
However, Christians believe that Jesus' was more than just a carpenter. Christians believe that he was the son of God, sent to earth to redeem mankind. So on a greater level, although his earthly occupation might have been carpenter, his heavenly occupation was much more. Christians believe that Jesus was both fully God and fully Man, so naturally, he had an earthly occupation but it paled in comparison to his heavenly one.
There is no evidence that can tell us the answer to any of these things.
If we accept the truth of the Gospels that are accepted as true by the Christian church (Matthew, Mark, Luke and John) we know essentially nothing about the life of Jesus between his youth and the time when he starts his ministry. This is a space of at least 18 or 20 years. For that time in between, we know nothing.
It is said that Jesus was a carpenter. From what I have read, the word used means someone who made houses -- not someone who was more skilled and made things like beautiful cabinets or pieces of furniture. However, we don't know who he worked with, how much he worked, how good he was, whether he built houses for rich people or poor, etc.
We really know very little about the life of Jesus because the Gospels do not pay any attention to his life between his youth and his baptism by John the Baptist.