Spoilers: This comment contains the solution.
It's super simple. First go outside(blue sky door) and collect the resources. Next, climb the brown ladder, climb down to one of the windows, and jump down the right window. This will somehow teleport you into the gray room, enter the glowing red door. It will give you a key. Now go back through the gray door, and climb the stairs. Feed the big stubborn thing and you use the key on the door and you have escaped.