In this work we use the Monte Carlo method to simulate the photoexcited carrier relaxation dynamics in suspended monolayer graphene to unveil the role of the different scattering mechanisms involved. The results show a strong activity of carrier-carrier and carrier-optical phonon interactions in the very early stages of the relaxation process driving the thermalization and cooling dynamics. The consideration of the coupling between the electron and phonon population reveals an intense damping in the cooling rates that is dependent on the pumped carrier concentration.