MBA for career advancement?

I (M22) currently have about 8 months (2023) of SWE experience working at a European tech company making roughly 12Lpa. I am planning of going for a MBA in the next 2-3 years but only if I get into a top b-school. I am highly ambitious and hope to climb the MANGA corporate ladder to a C suite/exec level position in the next 15-20 years. Will an MBA make sense for my goals and what sort of roles do tech giants usually hire for from top iims/isb and the likes? Is going for a MBA going to fast track my career or should I just grind the swe -> sdm -> director path with just a B.Tech degree ( Tier-2 private university)