How to go to Beijing airport at morning from Hotel near to Tian'namen East Station

What is the best way to go to the airport at morning because we have a fly at 8 AM to Shanghai and we need to be early for this fly with China Airlines and don't know the frequency of the Airport Express (please help to understand if the first train starts at 6:00 AM from Dongzhimen to the Airport T3? and the frequency of those trains.
Regards
RM from Costa Rica