You can get the training a lot easier than you could get the right to work in the usa. You can sit the FAA writtens in a few days. The path to an FAA ATPL starts with either a private certificate or a 61.75 private certificate if you already have an easa ppl. You will need additional specific training requirements. But it's very do-able. Right now the big advantage is that you have a visa so you aren't forced to use a school that will issue a visa, which opens your options up a lot. Find a local FAA instructor and fly with them, plus study the 14CFR part 61 requirements for pilot certification which will tell you in detail what you will have to do to get a CPL and IR done. Then hour build for atpl.
https://www.law.cornell.edu/cfr/text/14/part-61