You are not required to obtain an H-1B visa before seeking permanent residence. Your employer can start the process while you are in the U.S. with a TN visa. The issue will be timing as travel outside the U.S. can be an issue as a TN visa does not allow for dual intent. You can read more about the employment-based immigrant visa process at http://myattorneyusa.com/employment-immigration.
Answered on Nov 14th, 2016 at 2:40 PM