I like Carroll's [ https://www.preposterousuniverse.com/spacetimeandgeometry/ ] and indeed, you get to deal with intervals and worldlines in chapter 1.
It assumes you know or are ready to learn some differential calculus and how to read a formula with an integral but it (maybe a bit steeply) teaches tensors (and some aspects of vectors and scalars) across the first couple of chapters. Carroll provides some (quasi-)samples under the "Lecture Notes" tab, but the book itself has benefited from editing. He also supplies links to alternatives that can be had for free-as-in-beer.
https://en.wikipedia.org/wiki/The_Road_to_Reality
It is quite long and dense but explains the math from first princples like you want.