Be fast! Get down, get the cheese and keep walking to the right. There will probably be some wood to stand on. But be careful! The wood may collapse! If you can, walljump to the hole. Also, take note of the wood, as the last two bits tend for fall a bit early.
Make sure to secure the bridge with anchors before the mice knock it over! (normal mode shamans use red anchors and other mode shamans can use other anchors). Then you can balloon the other mice to the hole, or make a ramp up to the hole using planks.