Based on the moon example, it seems you define it as a set of principles you can base your decisions on? E.g. to get somewhere, you must minimize your distance. What makes something a first principle?

I'm asking because my understanding is that "reasoning from first principles" is just taking a step back, asking yourself what's really the goal and reasoning backwards. But it seems like you've got two different concepts (first principles and higher order thinking), which makes me think you've got it figured out more than I do.

First principles are not an ideology; they are more like laws of nature. Due to that, they are great both for reformulating a problem, and checking solutions.