Red Faction: Armageddon uses a clever method to set your inversion preference: w hen you first enter the game, it asks you to look up and then adjusts the controls based on that instinctive input.
That is a very clever way to work it out, I'm going to use it im my Godot stuff.
I don't remember if this was the game or not, but I tend to set the settings ahead of time, and I specifically recall a game getting to this sort of in-game mechanic of look up/ look down and reversing the setting I had previously set because it assumed I didn't already choose what I wanted (e.g. it re-inverted my reverted settings back to "normal").