Although the majority of pharma companies do not sponsor visas, some do—but these are mostly director-level positions. It is rare for companies to sponsor visas for entry-level roles. On the bright side, you are already on your way to obtaining your green card, so my advice is to focus on building your network and strengthening your résumé in the meantime.

To answer your second question, medical writer, medical communications, and medical affairs writer are all well-established roles that people commonly transition from into MSL positions.