Guangzhou Baiyun airport to high speed rail station for transfer to Changsha.

First of all, the high-speed trains to Changsha depart from GZ South Railway Station.
So according to your arrival time, you are advised to hire a private van from the airport and get to the railway station directly. Generally speaking, the fare is CNY 600 to 700 ay night.
By the way, the earliest bullet train is scheduled at 06:36. :)