On the Isle of Armor, according to NPCs, you need to do Max Raid battles in order to cause Max Mushrooms to grow. However, it's not clear if you need to win those battles, or if you just need to try them.
I ask because I have done several (4-5) Max Raids, lost most of them, and only found a single Max Mushroom in this time. I search all the caves and the forest between raids.