When I discovered plastic models in the early 70’s a lot of the kits around had dates on the instructions of 1950s. While plastic kits might date to the 1930s (FROG) I’m sure the post-WW2 economic boom spurred on the plastic-modelling hobby as we now know it. Certainly a lot of plastic HO train stuff was 1950s in origin! (Think Athearn, Roundhouse, etc)
I do not remember my first kit. There are several I remember from that time though. I had a ship (maybe a destroyer). It was plastic but it came with the parts to build an electric motor to put in the hull. It had the rotor, wire etc… Far beyond my skills at the time. Another was a Hawk AT 6. It was a yellow plastic kit if I remembered, maybe 1/72nd scale. I also remember the Super Marine racing float plane by someone in 1/72nd scale. Many models back then were expected to do more than sit still. Slot cars were going strong and people built their own chassis. Tamiya started the remote controlled tanks. Trains had been powered for years. Cox and others were making powered flying models. You could build a balsa and tissue airplane to fly.
I guess that depends on your definition of a model kit. If you consider lead soldiers, I think those are being cast back in the 18th century. I don’t know when the Royal Navy started the practice but the admiralty would have scale models of new ship proposals built in great detail. But I’m sure you’re talking about commercial model kits. Model railroading had kits coming out at the turn of the 20th century. Looking at some of the old catalogs from the 1920s and 30s, modelers could order rolling stock that they would have to assemble, usually a block of wood with some embossed cardboard or tin plate. They may have had to assemble the trucks and the couplers. Every now and then something shows up on eBay that dates back surprisingly earlier.
I recall that FROG was a very early manufacturer of what I consider model kits. Some were injection molded and some I think we’re in a material similar to bakelite. They were initially offered prior to World War 2. Monogram made model ships and airplanes right after World War II out of wood that needed some carving but I think a lot of them were pre-carved, with the equivalent of vacuum-formed engine nacells and other components. Do Pinewood Derby Cars count as model kits? I have no idea when they were first marketed.
If you want to narrow it down to plastic or similar material commercial kits that had to be assembled, I will say FROG is the leader. In America, I don’t remember if Monogram or HAWK or Lindberg (or somebody else) were the first. But I think that such models started hitting the shelves in the late 40s or early 50s.