The Leidenfrost effect occurs when a liquid or stiff sublimable solid near a hot surface creates enough vapor beneath it to lift itself up and float. In contrast, vaporizable soft solids, e.g., hydrogels, have been shown to exhibit persistent bouncing—the elastic Leidenfrost effect. By carefully lowering hydrogel spheres towards a hot surface, we discover that they are also capable of floating. The bounce-to-float transition is controlled by the approach velocity and temperature, analogously to the “dynamic Leidenfrost effect.” For the floating regime, we measure power-law scalings for the gap geometry, which we explain with a model that couples the vaporization rate to the spherical shape. Our results reveal that hydrogels are a promising pathway for controlling floating Leidenfrost objects through shape.