Can a level 10 player join a Giant mushroom battle?
No. A Giant mushroom needs a squad of 20, but a level 10 player can only field 15 Pikmin. You'll be able to join once you reach level 12.
Your maximum squad size grows with your level, and each mushroom size has a minimum squad you must field to start a battle. If your cap is below that minimum, you can't join β no matter how strong your Pikmin are.