The APU Controller will not engage the starter relay if the APU door is not sensed open more than 13 degrees. The door goes to 45 degrees on the ground and 15 degrees in the air (if running prior to takeoff).
Unfortunately, there are no warnings that the door is not at 45 degrees for ground operation. The larger opening, I assume, is required for proper cooling and airflow through the engine on the ground.
There will be an EICAS message if the door has been commanded open and the door has not reached 13 degrees after 60 seconds. If you only waited 25~30 seconds, you wouldn't even see this message.
I couldn't find any values for door opening speed, but it wouldn't hurt to wait 25~30 seconds to give the door a little extra time to completely open before going to START on the ground.