Transfer from US BB in NYC to Europe (London)

Hi all.
I started a new role about a month ago at a US BB (Citi/JPM/GS) in NYC on a very good team within markets (not specifically S&T, closer to PM) after having graduated in 2021. I have an enormous interest for working in Europe (either continental Europe or London, native English + Spanish so London probably ideal) but I’m not sure how to go about doing so. 

I applied to Msc programs before I got this new role and got into the LBS MFin program (full tuition at $80k), but I don’t think quitting this new role so early on is smart. I plan to work hard until around year end and mention my interest in making the jump to Europe. Is this too hopeful or would I have to likely wait longer? Is recruiting for new firms in Europe possible or would I definitely need a headhunter? Should I maybe defer and use a possible part time program as leverage to move over? 

Any recommendations or advice would be helpful, I would really want to move over soon.

Thanks!!