The only possible reason a European would consider coming to the US is to get enough multi crew jet time to go to Emirates. And most Europeans don't have a US ATP. Let's be crystal clear the problem is not a shortage of qualified pilots it's a shortage of qualified pilots willing to work for nothing.

Hint: Eliminate first year pay. It won't solve the problem but it will buy some time. If I were Republic or Mesa I would already be doing this because their contracts depend on putting butts in the seats. Unless they'd rather pay two Captains to covering the flying a la Great Lakes.