I'm an Australian living in the US on an E3 visa. I would like to get a green card, but we never win the lottery to move to a H1B and start the process. My youngest daughter was born in the US, and so is a citizen. Is there any way to get a green card without having to win the H1B lottery?
I got a green card while on E-3. Make sure your visa doesn't expire while you are in a no-travel period, as you might not be able to renew it if you have a pending change of status (or so I hear - was not applicable in my case).