Intrigued,
I would think it's safe to remove that "air" root this year.
Next spring, I would get in there and really work the roots. It appears there is a fairly large tap root going straight down. If possible, you want to cut that off flat, and work with the radial roots. Almost as if making a ground layer.
Birch usually produce nice radial root systems, so I think you can made a nice nebari with yours.
I posted a technique I used on a zelkova thread ("I'm going to make brooms"?) where I screwed the base of the trunk onto a piece of plywood, then spread the roots out across the board.
Good luck!