According to the current schedules, the first train arrives at 09:00 am (maybe schedules will change again in September).

AVE trains are very punctual so it's almost 100% sure you'll arrive at 09:00 am or even a bit earlier.

A taxi from Atocha to the aiport shouldn't take more than 30-40 minutes, but it depends on the traffic jams as Miguelito and Nativo said.

Be aware that airlines advice their customers to be at the aiport 2 hours before the flight departure.