Break into Tech PE/Tech VC?

Hey guys,

   I'm currently a mid-level SWE at one of Google/Meta - total compensation is around the 350-400k range (constantly changes due to fluctuations in stock price) and have about 3 YOE with a BS in math from a top 20 school. I've kind of always wanted to break into high finance and be able to utilize my math degree, but not sure how to go about that. I know of some people that worked at FAANG and then switched over to quant hedge funds/tech PE/tech VC...not sure if an MBA is required for this or not but I'm sure it wouldn't hurt to be able to network and build connections at a place like HBS/Stanford/Wharton. There's also the option for me to try to break into a place like Jane Street/HRT/Citadel Securities and I wouldn't need a grad school degree or anything, but practically speaking, this is going to be *extremely* hard and I'm not sure I'm smart enough to cut it at these places.

Money is also not a concern with regards to attending business school...although it would suck to have to give up 2 years of tech income and the potential compounded gains from that plus business school is expensive as shit. I just know that I don't really care for being a code monkey for much longer, and I want to be able to transition out of tech before I become a senior engineer and it's too late for me. I'm aiming to attend business school in about 2-3 years and need some sort of concrete plan to be able to get into a place like HBS/Stanford/Wharton because I know it won't exactly be a walk in the park and I should probably start preparing right now.

Any advice? Anyone here that made a similar switch? Can potential comp in high finance (with a tech angle) break 7 figures?? Seems like my cousin that's a tech VC in SF is doing really well for himself but he had a very unique path that's hard to recreate.