I know of a few pilots that are from Europe that fly here at UPS. One doesn't even have a U.S. passport, he uses his Dutch one instead.
UPS is firm about the 1,000 hours of P.I.C in a turbine powered airplane.
Once you have that, then it's a matter of networking. UPS has a good ole boy club here. You must have a UPS or management pilot recommendation, or you don't stand a chance. Sad but true.
That said, good luck!!