How to break into consulting off-cycle

Hi everyone,

I am a senior in a top undergraduate business program at a top business school. I interned this past summer at a PE megafund in a strategy role. I recently realized I think it may be more beneficial for me to pursue a career that is broader in responsibilities/role than in a strategy capacity because I feel my options are more limited, and I am not 100% positive about this. I want to break into consulting, and in the past have had final rounds at MBB. Any advice on how to break into consulting, or would it make sense to begin in the strategic role and look into consulting roles in my first few months? I was thinking of maybe even applying to 2024 roles and saying on my resume that I am graduating in December 2023. Thanks for the help!