"A unique mushroom-shaped hat found in the Mushroom Forest."
The Mushroom Hat is the first hat you can obtain in the game, regardless of level. It can be found in a Golden Chest, inside of a tree-house in Mushtown. In order to get to the tree-house, you must bounce up to it using two large mushrooms.
A guide on how to obtain the Mushroom Hat: https://youtu.be/0t3vnIZhG-E (Old video was terrible quality and also was moved)
Tips: Jump on the reddish pinkish mushroom first. Then jump onto the large orange one. Make sure to land as close to the middle (or "point") of the mushroom as possible. Zoom out all the way and look down.