We theoretically study the carrier relaxation dynamics in intrinsic graphene under pulse excitation taking into account optical-phonon (OP) scattering and carrier-carrier (CC) scattering. We consider the two limiting cases (a) where the CC scattering quasi-equilibrates carriers at all times, and (b) where the energy relaxation by intraband OP emission is dominant. We develop rate equations for the quasi-Fermi level and carrier temperature and calculate their time evolution. It is shown that in both cases the population inversion in the terahertz (THz) range can be achieved on the order of 10 ps after the pulse excitation. It is revealed that the threshold pumping intensity for the population inversion and negative dynamic conductivity in the case (a) is one order of magnitude smaller than that in the case (b) because of the thermal broadening of the carrier distribution by the CC scattering.