About math competitions for people just starting out, here are some off the top of my head... a lot of the middle school ones are actually organized by highschoolers, and a lot of the high school ones are organized by college students, hence their names. XD
Middle School contests:
Mathcounts (organized with school)
AMC 8 (organized with school)
EMCC = Exeter math club competition
LMT = Lexington math tournament
BMMT = Berkeley mini math tournament
MBMT = Montgomery Blair math tournament
High School contests:
AMC 10 & 12 (organized with school)
PUMAC = Princeton math competition
CMIMC = Carnegie Mellon math competition
HMMT = Harvard MIT math competition
BMT = Berkeley math competition
NIMO (this one is always online)
If you subscribed to the Daily Challenge newsletter, you'll get notifications about all sorts of upcoming math contests.
Most importantly, it's never too late to start. Don't worry too much about your scores, as they are just numbers. So just enjoy the problems and have a good time! IRL competitions are much more fun because you can meet people too lol. But since everything is online this year, you actually have the ability to "attend" math competitions that otherwise would be across the country! So that's cool.
