and no master builder. Can the last puzzle be solved with no builder on board??

No.

But it is possible to train a Master Builder late in the game if you get the right island event.

What event should I look for?

A mess on the beach

where by the beach
I see no mess

There is an Island Event (a storm) that will deposit another bunch of debris on the beach, similar to the one you had at the start of the game. Island Events are random, but it's very common to see that event happen at least once during any given game.

thanks