Which are the possible ways to get to the Shenzhen airport T3 from Dongguan?

From Shijie area, you can find the public bus line 71 to get to DG City General Bus Station, so you can take that bus to reach the general bus station. From the general bus station, you can find the direct buses for Shenzhen airport.
Since your flight is in the morning, it is suggested to go to DG bus station one day in advance.