The time setting of "Call it Courage" by Armstrong Sperry is not specific.  The reader is told that the story takes place in ancient times, but that is a super broad time frame unfortunately.  The only specifics that a reader is told are said in the first sentence of the story.  

"IT HAPPENED many years ago, before the traders and missionaries first came into the South Seas, while the Polynesians were still great in numbers and fierce of heart."

With that description in hand, it is safe to say that the book is taking place prior to the 1500's.  Europeans didn't start venturing across the Atlantic until just before 1500.  Polynesia is in the Pacific Ocean, so any European would have needed to round the southern tip of South America and continue to head west.  It's possible that Europeans could have sailed east from India and gotten to Polynesia, but that is unlikely.  India was the intended destination at that time, so any ships leaving India would head west to go home.  

Mafatu's tools and "technology" don't lend the reader anything date specific either, because many of those island tribes remained the same for centuries.  Best I can do for when the story takes place is pre 1500.