Sounds like the best and easiest option would be to land my first jet job in europe and build hours with the aim of moving west after a year or two?
I'd say stay in the EU until you have 1000 Turbine PIC. If you come here with 5000hrs on a 777, but no PIC time, you'll likely be looking at a regional carrier, flying a CRJ or an ERJ. You do not, I repeat do NOT, want to be at a regional carrier in the US unless you are at the very top of the payscale and seniority list. That's the only time it's worth it.