Really enjoy you channel, keep up the posts! My two cents and hope it helps. I found once I got into research you really appreciate the course work. As you stated, mathematics is built on foundational concepts and the there is alot of material to cover... personally I did a undergraduate and a masters course program before looking seriously into research (wanted a strong base). However, by showing initiative by asking for research and attempting it you maybe ahead of your group, with having a better understanding of what you like and also may help with university placement. Good luck.
I think the alternative to undergraduate research in mathematics is the William Lowell Putnam Exam which is one of the hardest math competitions in the world. If one places in the top five they're highly likely to receive research fellowships to some of the most prestigious graduate programs.
If you place top five in Putnam you're God-mode set brother. Literally a sure thing to get in everywhere. That test is all proofs. If you get like 20 points out of 120, that'll even be enough to put on your resume lol since the median score is 0.
