You would be surprised. But to say the truth, I trust the OpenSSH code a lot more than any VPN software that you can install to prevent direct access to it.
It depends a lot where you are from and what citizenship do you have.
If you are from Canada, some countries in the UE and a few others, it is pretty easy. You can even apply for the work permission when arriving in the USA.
For other countries, you have to find a job an go through the H1-B process (expensive for the company) and that can take a few months. Waiting for the green card will take even longer (4 or 5 years).
So most people that I know that came to the USA, they got a job in a large company (microsoft, etc) that applied for their H1-B. After arriving to the US, they applied for the green card themselves.
https://wordpress.com/plugins/trunc-logging
that would be interesting.