I think you can mostly credit Frank Rice. But a few caveats to start:
This is one of those tricky cultural questions where it clear something real is going on -- enough so that there's a scientific study that counts how many dinosaurs and dragons appear in children's bedrooms -- but still hard to quantify what 'typical "children's interest" subject' means. So even though we can point to the work of Samuel Griswold Goodrich, also known as Peter Parley, as the first to make a work about dinosaurs for children (Wonders of the Earth, Sea, and Sky, 1840) and there's a long history of paleoart and film and in-person exhibitions to stoke imaginations -- like Henry Osborn, who hired artists to make giant skeletons at the American Museum of National History, setting off a "paleoart fever" which lasted from the 1910s to the 1930s -- there's nothing in particular to distinguish the vast popularity of dinosaurs between adults and children.
I'm going to put the marking line as when children started to play with dinosaurs. And it is quite true, before the year I'm about to discuss, dinosaur toys were not generally a thing: the idea that the market even existed had to be realized, which I think gives good evidence the 'typical "children's interest" subject' threshold hadn't been reached yet.
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New York, 1955. Time Magazine calls Louis Marx the Toy King. His company, Louis Marx and Co., is at its peak, by far the dominant toy manufacturer in the United States.
Frank Rice was chief designer, and the 1950s had yet another wave of dinosaur fever. He went to the American Museum of Natural History to get inspiration (the same place Osborn made dinosaur exhibits in starting in the 1910s) and proposed a new playset to his boss, Ed Hjelte.
Hjelte was convinced, but it was a hard sell to anyone else at the company, including the Toy King himself, Louis Marx. Children liked dinosaurs, but unlike a Western town where kids could envision a shootout at high noon, Marx and others thought dinosaurs lacked "conflict" -- there would be nothing to role-play.
However, one of the sculptors on staff, Phil Derham, was given a shot at making a set in order to "keep busy" (he was so talented there was concern he would be poached elsewhere without consistent work), and three groups were made designed for dime store bins.
While it was possible to obtain one of the Marx dinosaurs in 1955, things hadn't quite gotten hot yet.
(Interlude: feel free to watch this minute long video showing a 1956 toy fair in Yorkshire giving an idea what toys were like that year.)
Marx rolled out a fancy painted scene (by Cliff Freeland) to go with an exhibition at a 1956 Toy Fair. It was a big draw to retailers, but it would have been hard to manufacture in plastic; a new process called vacuum forming was used to put some in production but they could only be made in limited quantities for displays.
In the meantime, Marx still felt the "conflict" was lacking, and they needed someone to fight the dinosaurs. Who else but ... cavemen? So while sales had already started humming, Derham then produced a set of cavemen to go with the dinosaurs, so now they had someone to battle. This was put into a full 1957 set -- no longer the individual models -- which was launched for huge sales, and children's play was changed forever.
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You can see pictures of Marx Large Mold Group PL-749 here (the very first dinosaur toys Marx made) where you can click further to get far more detail than you'd ever think possible about a set of 1950s toys.
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Debus, D. E., Debus, A. A., Morales, B. (2013). Dinosaur Sculpting: A Complete Guide, 2d Ed.. United States: McFarland, Incorporated, Publishers.
Kern, R. S. (2020). Marx Toy Kings Volume I. Playset Magazine.