PART 135 domestic charter/ non green card holder?
You must have the right or approval to work in the US in order to...um...work in the US. Doesn't matter what the job is. A residency permit ('greencard') is one way to get that approval. Citizenship too, obviously. Some other business/work visas but they typically require investment or sponsorship. I very much doubt any 135 will be willing to try sponsorship since that often means showing that there's a shortage of some specialist skill. Not really the case this month for pilots...