I don’t think that TileMapLayer is a correct choice. Try using a TextureRect node (or any other Control-type node that has a texture property will work) with an AtlasTexture resource as a texture. Then you can define which region of the texture to show.
As an alternative: the quick hack would be putting a Sprite2D under the Button and abuse the animation functionality (see the Frame value 4 corresponding to the five on the dice).