I stand to be corrected but I do not believe that the nav bar can be set to auto-hide by default. You can search out and upvote "auto-hide nav bar" (or something like that) in Windows Feedback if you want to add your voice to those wanting this functionality.
I think it's a no-brainer, at least on the start screen, that you should be able to set the phone to default to the nav bar being hidden.