@TowerDog H1B / EB-2 Visa (or similar) for skilled workers still exist. It's an easier process in Canada and Australia for us Europeans though.
Marchisio as already stated, it comes down to
one option (GreencardLottery has a 2% chance of winning) and that is
marrying an US citizen OR permanent resident (Greencard holder)
You can then apply for a visa, to become permanent resident (which is enough to work for an U.S. airline) and after some years you could become US-citizen.
The FAA-ATPL costs about 13.000€, the conversion now is a lot more complicated now adays
But why do you want to work as a pilot in the states? I agree it's a great country , but for pilots Italy is a good place, isn't it?.
I mean here, after 2 years of flight school and with 200 hours you fly A320 across Europe or 767 long-haul charter and make 3 times what your friends make. With age 22.
The US market has a longer career path, and is less
plannable. There are no ab-initio programs or pilot schools run by airlines.
Instead collecting hours as flight teacher, firefighter planes, commuter planes etc. until you can get onto something with 50+ tonnes ZFW and make a decent income.
And please don't get me wrong. I think MPL and low experience pilots in big airliners are not the best way (though I am one myself), but as I said, it makes career here MUCH more plannable. Your income is on a good level fast and you can move on.
Although the big numbers the majors pay now, are not common anymore in EU...
Good night.