@bluebayou
Cheers to you.
In my book, and I am sure in the book of other people holding PhDs, including professors on the admission committees, “building resume” means doing research and publishing papers, and getting them cited by other scientists, and not sitting in MS program. Respectable math graduate schools, mostly, do not even have MS program for pure math!
If this application season doesn’t pan out, I hope my son will choose exactly that path: more research and more publications.