Business clubs affect on recruiting

Writing this as I’m stressed about how a failure to get into business frats/elite clubs will affect my recruiting chances. I go to a strong semi-target but it’s liberal arts so no b-school undergrad. Because of this, business clubs bridge the gap. I seem to see most people who succeed in recruiting be in business clubs/frats.

I have a 3.75 math major, did a search fund and short summer internship at a PE shop, and am part of a student fund on campus (limited alumni network though). I guess I’m just feeling stressed networking will be much harder as I won’t have a business frat/elite club network. Will a lack of these extracurriculars really hurt my recruiting chances? I feel like getting referrals could be harder as I wasn’t a part of many alumni’s student orgs.