I remember there being a lot of forest in and around Berlin. Even as late as I got there (78-81) you could still see a lot of the damage from the war.
The engineers carried portable saw mills with them and there was apparently ample trees as for instance, they built camps for displaced persons and for war criminals. They also built a large mess hall for the Potsdam conference.
They used wood from trees sawed locally. They also hire Germans to do a lot of work and according to Daddy, they were extremely hard workers.