USA PE Recruiting options/ Strategy as a UK IB analyst with a green card

I'm a few months away from starting my Full-Time Analyst position at a Bulge Bracket firm in the London office. I am UK citizen, born and raised. However, my circumstances have recently changed as I married my wife (I know I got married early lads lol), a US citizen, and have obtained permanent residency (green card) in the USA.

While I don't mind spending my initial analyst years in the UK, from a logistical standpoint, it would be more practical to transfer to the USA office, preferably during AN1, since my wife resides in New York City. Although this transfer would be ideal, I'm not overly concerned if it doesn't materialize, as my primary focus is on transitioning into PE after my two-year stint as an analyst.

Given this somewhat unusual situation for an analyst, I'm seeking advice on the feasibility of moving to the buy-side in the USA in terms of recruiting strategy for someone in my situation. How should I approach this in my current circumstance? 

Any advice or insights would be greatly appreciated!