Assuming you'll catch the first MRT, you'll get to Taipei Main station at 06:34
You should probably get back to TPE airport by 08:30, which means taking either the 07:45 or 08:00 "express" MRT from Taipei Main Station
80 minutes - barely enough time to walk to Fuhang Soy Milk and their long morning queues - but you'll get to stretch your legs and have a Taiwanese breakfast experience