I recently bootstrapped myself from your level to algebraic geometry — enough to read an annotated version of Einstein's paper. If I had to do it again, I'd just skip to the parts that worked: (1) hit up Michael Penn on YT, but work all the problems he works; and, (2) learn GA, I like MacDonald's "Linear and Geometric Algebra". I'm going to be honest: unless you do the homework, you can't learn the math.
I learned Penn because it's "real" (mainstream) math & lets you read in the same language; I learned GA because it's designed to proselytize to other mathematicians & deliberately presents serous ideas in very approachable ways.
Isn't general relativity framed in differential geometry, not algebraic geometry? All of Einstein's papers on special relativity use high-school algebra and calculus.
Yes, GR uses differential geometry; however, a good (mechanical) understanding of any exterior algebra helps when working with tensors; and, I found GA much easier to understand than algebraic & differential geometry, when starting out. The idea is to familiarize yourself with learning math. The actual math of the GR paper is pretty straight forward: it's the physics which is so mind bending.
I learned Penn because it's "real" (mainstream) math & lets you read in the same language; I learned GA because it's designed to proselytize to other mathematicians & deliberately presents serous ideas in very approachable ways.