My new job starts on June 1. Can I go to the port of entry now? Is there time requirement for getting the TN-visa at the port of entry, within 1 month or 2…months before your job starting?
-May be not. After you enter US with TN status, you may need to work for the employer immediately. Here is a DOS website about TN visa and it seems you need to get the TN visa at a US Consulate outside US or change your H1 status to TN within US: