Studying superdiffusive thermal transport is crucial for advanced thermal management in electronics and nanotechnology, ensuring devices run efficiently and reliably. Such study also contributes to the design of high-performance thermoelectric materials and devices, thereby improving energy efficiency. This work leads to a better understanding of fundamental physics and non-equilibrium phenomena, fostering innovations in numerous scientific and engineering fields. We are showing, from a one shot experiment, that clear deviations from classical Fourier behavior are observed in a semiconductor alloy such as InGaAs. These deviations are a signature of the competition that takes place between ballistic and diffusive heat transfers. Thermal propagation is modelled by a truncated Lévy model. This approach is used to analyze this ballistic-diffusive transition and to determine the thermal properties of InGaAs. The experimental part of this work is based on a combination of time-domain and frequency-domain thermoreflectance methods with an extended bandwidth ranging from a few kHz to 100 GHz. This unique wide-bandwidth configuration allows a clear distinction between Fourier diffusive and non-Fourier superdiffusive heat propagation in semiconductor materials. For diffusive processes, we also demonstrate our ability to simultaneously measure the thermal conductivity, heat capacity and interface thermal resistance of several materials over 3 decades of thermal conductivity.