There are several issues here.
First of all, if you have a frozen ATPL or fATPL, you don’t have an ATPL. You have a commercial license with the ATPL theory completed.
Secondly, you will need to get familiar of the process to convert a license. The US and Europe have a reciprocal agreement. Knowledge tests and practical tests must be completed to convert the equivalent license. It goes both ways. Someone with an FAA certificate would need to complete the 14 ATPL exams plus the practical exams. EASA to FAA requires taking the equivalent exams.
There is an exception to this, and the FAA will allow you to get a private pilot certificate based on a foreign license under FAR 61.75, hence why you will have to resubmit your IACRA with private pilot. If you want a commercial certificate, you’ll need to pass the theory exam and practical test. If you have an unrestricted ATPL, you’ll need to also pass the ATP-CTP course before you can sit the ATP knowledge test.
Once you get the 61.75 certificate, you’ll need to pass a flight review with an instructor in order to fly. I recommend getting familiar with the FAR/AIM, and sections 61 and 91 specifically. It’ll save you a lot of grief.
As far as doing the verification all over again, you’ll have to contact the local FSDO. Also, the FSDO does not handle visa issues, aka they can’t tell you if you have legal status to work or not, the only can tell you from a regulatory side if you have the right certificate to work or not.
I hope that helps.
To the first reply in this thread, I’m not sure what status the OP has but I wouldn’t just assume that he has a green card or citizenship. My guess is a B1B2 visa but that’s for the OP to decide to share or not.