When a Leidenfrost droplet floats on its own vapor layer, the interplay between vapor pressure, surface tension, and gravity determines its shape, and in the stable regime the underside of the droplet exhibits curvature inversion. Using interferometric imaging, we observe a different behavior for a levitated hydrogel sphere. Curvature inversion appears briefly after deposition, but the continuous vaporization process removes this feature, leading first to an oscillatory regime and eventually to a steady state without curvature inversion. We demonstrate the essential role of vaporization in shaping the hydrogel underbelly, where direct mass loss has a stronger influence than the balance between vapor pressure and elastic forces.