Wait for the shaman to attach the large piece of wood and build something up to the cheese. It is not recommended to make the wood fluctuate, because this is very hard to do and in most cases the wood falls off the map then, which will make it almost impossible to return to the hole.
First, attach a red-anchored small plank to the piece of wood to stabilize it. In hard mode, put an anvil to the middle, this is normally enough. Then attach a c-anchored large plank to the wood in order to make the mice climb the platform and get the cheese.