Strategy at BB to VC/GE

I'm currently an associate with 3 YOE on the strategy team in the commercial bank at a major BB in NYC. My team focuses on virtually everything strategy related (product roll out, customer acquisition/retention, etc) for pre-series C funded companies in the tech and healthcare industries.

I've done a lot of research on potential career paths and know I want to break into VC/GE at some point. Has anyone made that jump before and what would be the best path forward? Should I get an MBA or would I be able to jump straight to a local firm? I don’t necessarily want or need to have an investor role. I could see myself working on the originations side / business development or even breaking in through a corporate function if it would allow me to get to the investor or originations side in the future.