HF Possibility With 'Atypical' Background?

Hi all - I’m looking to get a quick pulse check on the feasibility of transitioning into the MM/SM hedge fund space.

I graduated from a target school and have ~4 years of experience: two years in investment banking at a bulge bracket, and I’m now approaching my second year in a principal investing role. While my current firm isn’t a traditional buy-side platform, we invest long-term capital and operate somewhere between a financial sponsor and a strategic. As a result, we evaluate a high volume of opportunities but rarely transact, given there’s little urgency to deploy capital. My work is heavily focused on diligence and investment analysis, but lacks the pace and repetition of execution you'd typically see in a more active fund environment.

Given this background, does it make sense for me to explore roles in the hedge fund space, particularly at MM/SM platforms? Would appreciate any perspective on how transferable my experience might be. Really starting to regret not taking the classic 2+2 PE route.