It's easy to complete the game and never have a Master Builder, especially if you have a lot of villagers working on the construction projects. There is only just so much work to go around.

Unfortunately, in v1.0 the only way to train a builder after all of the construction puzzles are completed is to hope for an Island Event that washes more debris onto the beach. In v1.1 you can train builders anytime by having them fix the huts that they built.
The bug that causes villager disappearances has also been corrected in v1.1.