people being able to recreate the same effect over and over again using natural interactions with no outer agency. Nothing they feel inside themselves to prove that there's anything other than nature interacting with itself, and no need to call on any outer power.

Like, say, gravity. If you have it, and you drop something from a height, it will always be drawn down--it will fall towards the source of gravity--without any further action on your part other than letting the object go. And it will do it every single time, without fail. No god, no 'power' or hands of fate involved. Just the result of a natural phenomenom caused by the rotating of the planet you're on.