In today's world the presence of ozone in the stratosphere is the reason for the stratospheric temperature inversion which keeps a lid on the troposphere.
But before the Great Oxygenation Event there wouldn't have been enough oxygen to create ozone in the stratosphere. Which leads two questions
1) Would the top of the troposphere have been much higher?
2) If there's no stratosphere to keep wet air down in the troposphere would more water have got into the upper atmosphere where it can be dissociated by UV light and the hydrogen lost into space?