Transitioning Enlisted Military looking to break into PE eventually, but for now get my leg in.

Currently AD with a BS in Health Science from a non-target and accepted to NYU MS Quant Mngmt program. I work in the medical research field atm for the military. I transition out next year October, which will be off-cycle. I am planning on applying for the Veteran Associate Programs at various firms; GP, BAML, JPM... I have no finance background other than what I will learning in my MS starting in the Fall & some Coursera finance courses. I understand connections are key. I am looking for advise on how to better position myself for success. Thanks.