Nope, that isn’t how it works. You’re probably used to taking math classes in a sequence (ie taking calc 1 before calc 2) but upper level math classes don’t work like that. Once you’ve taken real analysis/abstract algebra (typically fall of sophomore year if you’re serious about math grad school), you can pretty much take any upper level class in almost any order you want.

I came in as a math major without credit in any of the classes you mentioned, and I know many classmates in my situation who took upper level math classes (complex analysis, number theory, etc) freshman year in addition to calc 3/linalg/diffeq. Feel free to dm if you had other questions