what's the chance of switching from F500 FP&A to Big Four Financial Advisory?

I am an accounting&finance student graduated from a top accounting program. I accepted an offer from a Fortune 500 company for a typical entry level FP&A position. Most of my friends went to the public firm (mainly the Big four). I like the company's culture and its people, more importantly the company is willing to sponsor my Visa, but I am worried about the limitation on exit opportunities in the future. I want to expose myself to different challenges and learn as much as possible while I am still young, also given that my time in US is limited, so I really want to get the most out of it.

I wonder how hard it is to change job after 2-3 yrs in F500 to Big Four financial advisory. I am thinking about something relevant to corp finance or accounting. I know Deloitte has a department called Accounting&Reporting Transformation which I am very interested in. I went to their office for interview but I didn't get the position. I am not a big fan of Audit or Tax, no offense, but I think I might be more better off if I stay as a FP&A than doing audit/tax.

So How can I leverage my experience in F500 FP&A to get into financial advisory in Big Four? Thank you