Quant Seeking Advice For Moving To Trading Shops/HF

Hi WSO,  a little background of myself. I graduated from a nontarget but accepted to a top tier master of financial engineering program and now i am working as a capital market quant(front office/middle office) in a bottom BB(think RBC, WF), I also have a military service background which makes me a very unconventional quant in my firm (my average coworkers are of STEM phd background). I believe my mathematics knowledge foundation is not as solid as my coworkers but is enough for the job, I'm also a quick learner. I represented my undergrad+master school to compete in multiple large trading competitions(manual trading +algo option trading, I love designing trading algos) and placed very well.

I really want to break into trading shops(like SIG/IMC/Jump) or quant hedge fund(like Point72) in my future career. Given my background I mentioned above, should I first work couple years at my current firm, then exit to a front office quant position in a top BB(BAML above) then finally go for buyside firms?  Or I can get myself to a front desk position, work for couple years then apply directly for buyside?  Any advice is appreciated!