A future Galactic Supernova (SN) explosion represents a unique opportunity to probe both the physics of SNe and fundamental particles, such as axions and Axion-Like Particles (ALPs). The Large Area Telescope (LAT) aboard the Fermi Gamma-Ray Space Telescope will be instrumental in revealing possible gamma-ray signals induced by ultralight ALPs thermally produced in the SN core and converted into high-energy photons in the Galactic magnetic field. In this talk I will assess the physics potential of the detection of an ALP-induced gamma-ray signal, evaluating the capability of Fermi LAT to reconstruct the ALP-photon coupling, taking into account uncertainties on the modeling of the Galactic magnetic field. Moreover, I will show that, if ALPs simultaneously interact with photons and nucleons, the observation of an ALP-induced gamma-ray signal would be extremely useful to directly probe the physics of the SN core, for instance revealing the presence of pions in the core or allowing the reconstruction of the average core temperature in the first seconds after the core collapse.