Mine keeps his on, but it has a chin strap! It’s actually really good - it has a wide brim so his face is properly shaded. We live in the uae so a proper hat makes a difference! https://www.amazon.ae/gp/aw/d/B0C2TZKBMP?psc=1&ref=ppx_pop_mob_b_asin_title
Tied on with ribbons or elastic is the only way we can keep hats on and even then we have to battle!
Only stays on for me if it has a strap!