I've seen this style of Pith attributed to all of those generations, but I do not know how to find a definitive date.
Vintage U.S. Khaki Pith Sun Hat / Helmet with chin strap and liner brackets
Vintage Pith Helmet
Pith Helmet, US unissued New Pith Hat 1960s - Omahas Army Navy Surplus
Vintage Pith Helmet
Rothco Campaign Hat: Military Apparel Accessories: Clothing, Shoes & Jewelry
Genuine US Military Vietnam war Era Pith Safari Sun Hat Waterproof
American 47th New York Summer Sun Helmet 1800s . HU1068 - Time Traveler Militaria
LIBERTY MOUNTAIN Pith Helmet (Khaki) : Clothing, Shoes & Jewelry
British Empire Pith Helmet - Khaki
VINTAGE MENS PITH HELMET SUN SAFARI HAT MADE INDIA SIZE 7 1/4 British Khaki
Vintage 1950s Ihi Sunproof Hat Military Pith Sun Helmet Khaki Drill India Safari