You must have the right to live and work in the USA (a greencard or some acceptable class of visa). That is the most important thing, outside of that you will have to pass a 10 year background check to work for an airline, this can be difficult if you are not a US citizen and have resided outside of the US during the last ten years, it is however not insurmountable as you can get a letter from the authorities in your home country stating that you are of good character and have never been convicted of a crime, further more you can get documentation from schools and colleges that you have attended to add to the file, this should suffice as long as there is nothing illegal in your past. To Work for a Major airline a College Degree, while not mandatory is pretty much required. If you have a degree from Europe then this will do. Lastly the flying is of a very high standard and the experience requirements are high, typically major airlines hire people in the 4000hr plus experience range and the ideal candidate that they are looking for is some one who is already flying as a captain with another airline (a regional jet/turboprop operator for instance). There are a few exceptions like the one or two 400hr people that United Airlines take on every so often but you would have better odds on the lottery if you were holding out for one of these jobs.
Good luck and keep in mind that from your first flying lesson through all of your ratings, working as an instructor, getting to a regional and finally a major is probably going to take in the region or 6-10 years.