As of now, TSA will not clear you to get a type rating for a 121 carrier unless you are obtaining it on behalf of your foreign employer, as in like come to US, get your TR and then GTFO. You gotta be a US citizen or greencard holder in order to pull it off.

H1-B would work for applicants that would like to remain in US for a limited time while doing paid practice, flight instruction for example.

You can thank 9/11 for that...