These two cities are so close to each other that it just takes you 30 minutes from Tianjin to Beijing South Railway Station by train. So, I think you could depart early in the morning and then arrive in Beijing around 07:30. Then, you could take the subway Line 4 to Xidan to catch the airport shuttle bus Line 2 to reach the Capital Airport in one hour. Or you could transfer to Line 2 at Xuanwumen and then get off at Dongzhimen, where you could catch the Airport Express to reach the airport in 30 minutes.