Where did the boy come from?

Since no one knows what happened in real life, this film is fiction. The film tries to steer the audience into the "They went mad from mercury poisoning." He even says he looks like Charlie. Charlie is the name of James's child.

I had the same question. It was a truly puzzling development in the story, as there seemed to be logical explanation for how a child could get onto the island.

I think he's on the boat with the 2 men