Core-Collapse Supernovae (CCSNe) are important phenomena in the scope of nucleosynthesis and, as the final stage of massive stars' life, they are key processes in the understanding of stellar evolution. They also are the birthplace of neutron stars and black holes, therefore they play a major role in the modelling and understanding of compact object mergers. While CCSNe have been observed for a long time, it is mainly through electromagnetic radiation. This channel gives us precious information about the explosion energy and nucleosynthesis, but fails to inform us about the collapse and initial explosion mechanism. While other observational channels are becoming available, through neutrino detection and gravitational waves, we are still waiting for a galactic CCSN to get an appropriate signal giving us insight on the explosion mechanism. We, therefore, have to rely on simulations for now. CCSN simulations have been performed for 60 years, improving decade after decade, and are now able to produce systematic self-consistent explosions. Several parameters impact the final outcome of our simulations, originating from different physics treatments, such as the gravity, neutrino transport and interactions, micro-physics through the equation of state, or magnetic fields. To understand the explosion mechanism behind a CCSN, we need to study the impact of each of these uncertain pieces of physics. In this thesis, I focused on the impact of the emission of heavy-lepton neutrinos and axions on the explosion, concentrated on the early proto-neutron star cooling. I explain details of the CCSN process, as well as some of the particle physics I focused on. I show how a change in heavy-lepton neutrino and axion emissions can accelerate the early proto-neutron star cooling and subsequently help the explosion.