Seeing as clay and branches are limited, why not introduce another method of creating brick?
Mud brick:
1. Create a wooden mold (a mold could produce multiple bricks).
2. Insert soil or sand, water, and straw or plant fibers: 1 soil/sand, .5 liter of water, and 1 straw/plant fibers per brick.
3. Let it set
4. Obtain mud brick
Can be used in substitute for regular brick.