Yamanaka Kumiki Works is a Japanese manufacturer of puzzle boxes. The company also makes this intriguing cow puzzle, where you have a series of unlikely shapes that can be assembled into a bovine:
Could your kid figure that out? I’m not even sure if a practicing industrial designer would get it right on the first try, but it would be fun to see.
Sadly the company does not have any U.S. presence, but they’ve apparently been making these animal-puzzles for decades. You find vintage examples on Etsy, like this elephant puzzle (with no video showing you how it goes together) from the 1950s.