Breaking into PE-VC/Consulting after tier-1 masters programs

Hey everyone,

I am Sarthak- a final-year economics undergrad from a tier-2 college in India. (feel free to connect on Linkedin- Sarthak Dave) 

I have reasonably good co-curricular and leadership experience, recently interned at a PE firm based in London, although the role was back-end research.

I wanna break into PE-VC/Consulting soon, ideally with a global experience and I was considering going for tier-1 masters programs in the US/Europe straight out of college (fall 2023) without any full-time experience as the opportunities/access here in my university and the pay too aren't really synced with what I want.
Will such a masters program be worth it and help me get where I want- front-end consulting/PE-VC/Asset Management or should I try and gain work ex if I have a choice?

Would appreciate everyone's input on the same!

Thanks