YMH:
You may be issued a FAA private pilot certificate on the basis of a foreign licence under the provisions of
FAR 61.75
FAR 61.35 contains the eligibility requirements to take knowledge tests. (formerly "written" tests)
FAR 61.123 requires an endorsement from an authorized instructor to be eligible to take the Commercial pilot knowledge test. Note that there is no longer any flight experience requirements to establish eligibility to take knowledge tests. Note also that, except for graduates of an approved course,
FAR 61.129 requires at least 250 hours total time to be eligible to take the commercial pilot practical (flight) test.
FAR 61.153 covers the general eligibility requirements for the issuance of an ATP certificate. Note that no endorsement from an instructor is required to take either the knowledge or practical tests except in the case of a retest after failure as per
FAR 61.49
To summarize the steps to be taken to get your FAA ATP certificate:
1) Get your FAA private on the basis of your SA private. If you have an instrument rating, see that this is noted on your FAA certificate by providing an FAA instrument rating knowledge test report along with your SA private with instrument rating. If not, then consider getting one sooner, rather than later.
2) Self study or take a ground course for your commercial pilot knowledge test. You will need an endorsement from an instructor to take this test.
3) Complete the required training and pass your commercial pilot practical test.
4) Aquire the flight experience required for your FAA ATP as per
FAR 61.159 This flight experience may be gained anywhere in any registry of aircraft as long as it is properly logged as per
FAR 61.51. Only the required training and endorsements must be from a FAA authorized instructor. No instructor endorsement is required in order to take the ATP knowledge or practical tests.
I regret that I am not conversant in the issues of enrty visas or the security requirements related to foreign pilots who wish to train in the USA. If you require advice in this area, there are likely many others on this forum who have "jumped through those hoops" and are familiar with the process. All we USA CFIs are required to know is that we must assure that foreigners have been cleared by TSA prior to the commencement of training for a higher certificate or rating. I'm only sure it has the potential to become a pain in the rear!
The above should not be considered authoratative in any respect. This why I linked all the applicable regulations that I quote. You or someone else may interpret these regulations differently and possibly more correctly. After all, "some anonymous guy on the internet" is hardly an authoritative source. I do hope you will find the references useful though and wish you the best of success!
Best regards,
Westhawk