[fantod]

You don't really need to know calculus (derivatives and such) but it's true that big O notation requires some sort of "asymptotic thinking" which is probably only explicitly taught in a calculus course.

[Retric]

That’s part of Pre-Calculus or general mathematics coursework at most US high schools.

Beyond that it’s a very simple idea you can cover at the same time as your doing Big O notation in the first place.