I am a non-US citizen with a consulting/teaching background and am looking for a job with a visa sponsorship. I earned two master's degrees (Women & Gender studies and literature) and a teaching credential from California, but obtaining a visa as a non-tech person is a complicated process.
I want to send out networking emails to strangers who work at a company that I am interested in working for (I'm only applying to large tech and consulting companies, like Google and Deloitte, that sponsor a high volume of visas).
My question is this-- should I mention that I need a work visa in my first email to these strangers? Do you think this shuts down potential opportunities?