As we witness the fall of the American empire, it's the perfect time to read the Foundation series (by Isaac Asimov)

Not every aspect of every concept needs to be fully interrogated at every moment. Especially since psychohistory is essentially taking the idea of "social history" or "history from below", and applying the law of large numbers to create something predictive, but only over a sufficiently massive population. I'm pretty sure that was actually mentioned in the first book. That the only reason psychohistory was able to work at all is because it was averaging the actions of the entirety of the Galactic Empire, complete with population of one quintillion.

The obvious counterpoint to that is the same as the counterpoint to "history from below" in general, "great man theory". So after a few stories of the Foundation doing their thing, in comes a sufficiently "great man" to frick things up. And to make clear that that's what's happened, Asimov uses a recurring element that I'm pretty sure was established in the stories in the first book, where a recording of Seldon is played from time to time, and always includes the percentage chance that the Plan is on track, with the number decreasing every time. So yeah, the fact that psychohistory was just a numbers game is pretty well established in the first book alone. The bit about the Second Foundation existing and operating behind the scenes to keep the Plan on track wasn't established until the second book, but like I said, not every aspect of every concept needs to be fully explained, front and center, right off the bat.