Well, we know who didn't build it. Namely the Hovitos. As the novel has it, the Hovitos revere the Temple of the Chachopoyan Warriors (as it is called there), but are not the Chachopoyan Warriors themselves although there's nothing to say they aren't descended from them. They certainly know of the idol and want it, and kill anyone who would dare enter to claim it before they can. The reason they were helping Belloq is because they believed that after Belloq took the idol from Indy, he would give it to them. Which of course he doesn't, being Belloq.
All we really know about the temple and its builders, the Chachopoyan Warriors judging by its name, is that they were very crafty trap designers who thought of every conceivable contingency, not only installing stuff to kill you while you were trying to reach the idol, but installing the final "failsafes" (the collapsing ceiling and the entrance-blocking boulder) to make sure you wouldn't escape with your prize if you got that far. And this isn't merely from observing the sequence in the film; Indy marvels at how creative the Chachopoyans were every step of the way, both going in and out of the place.
About the only other stuff we learn about this scene is some backstory on the Forrestal character, how he is connected to Indy, and how and when Indy decided to pick up where he left off. If I'm remembering correctly, Forrestal was a professor at the same college as Indy, and after he went missing in Peru, Indy searched his papers and found a piece of the map to the Temple of the Chachopoyan Warriors among them, which sparked his interest. So, viewed this way, Indy's mission was to both obtain the idol and discover what happened to Forrestal. Forrestal himself is described as being a fairly bookish guy, not an outdoorsman at all, and upon finding his speared corpse Indy sadly tells his colleague he "should've stayed in the classroom."
Which, of course, means that for a bookworm with almost zero field experience, Forrestal actually finding the temple and making it as far as the first trap is a feat unto itself. No wonder Indy told Satipo he was "very good." He hadn't thought the old boy'd had it in him to make it as far as he did!