Best path to transition from BA to Quant Trading

Graduating from UVA this May with a degree in electrical engineering. I'm starting at Capital One this fall as a Business Analyst, not sure which team I'll be on yet. Pretty excited, but some of my friends are going into S&T and I've been becoming interested in the markets and the quantitative side to trading.

What would it take to transition to a prop shop or hedge fund or bank on wall street? I know Capital One does a little bit of this kind of work in oil and gas and FX markets, but I don't know how easy it'll be for me to move over to that side of the company. Should I just send it and recruit at trading firms in a few years? Would it help to go back to school and get a masters in math or data science? How should I be tailoring my resume for this line of work?

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