How do I break into IB, PE, or VC as a science major from a non-target school? Should I pursue a Master of Finance?

Hi all, I'm a rising senior at a good school (but non-target) studying Kinesiology (Exercise Physiology...yes, I know very random). I wanted to be a sports performance coach heading into college, but I started developing a passion for finance in junior year. Breaking in cold turkey is obviously a stretch, so I was looking to maybe further my educational background with a Master of Finance. I know there is a lot of deliberation over whether or not an MSF is a waste of money. Got a great internship at a small VC firm for the summer. I will score a 650-700 on the GMAT with average quant scores and excellent verbal scores (again, not ideal...I know). My undergraduate GPA is a 3.3, but I have gotten solid grades in finance/accounting courses.  Target schools are probably out of reach for grad school as well (Fordham or Baruch are the most likely destinations). Getting a CFA will definitely be in the cards. With all that said, what do y'all suggest I do now to better my chances of breaking in? Do you suggest pursuing a Master of Finance? Any stories from people in the industry coming from non-target schools and majors?