Journey - Beijing airport to Tianjin

it takes 30 - 60 minutes for the customs/immigration.
the bus from the airport to Tianjin stops at that time. so you can take an airport shuttle bus night line to Beijing Railway Station. there you can catch a train No.2601 departing at 04:22 to Tianjin. It takes 1 hour and 46 minutes to Tianjin.
If you feel tired and you don't have to rush to Tianjin, you can take the airport bus night line to Xidan, and check into a hotel for a few hour's sleep. In the morning, take a taxi or subway to Beijing South Railway Station to catch an inter city high-speed rail to Tianjin.
Alternatively, you can stay at a hotel in the airport and take the morning bus to Tianjin. the first one leaves the airport at 07:00, and it takes 2.5 hours to reach Tianjin.