Investigation of the non-equilibrium dynamics after an impulsive impact provides insights into couplings among various excitations. A two-temperature model (TTM) is often a starting point to understand the coupled dynamics of electrons and lattice vibrations: the optical pulse primarily raises the electronic temperature T(el) while leaving the lattice temperature T(l) low; subsequently the hot electrons heat up the lattice until T(el) = T(l) is reached. This temporal hierarchy owes to the assumption that the electron-electron scattering rate is much larger than the electron-phonon scattering rate. We report herein that the TTM scheme is seriously invalidated in semimetal graphite. Time-resolved photoemission spectroscopy (TrPES) of graphite reveals that fingerprints of coupled optical phonons (COPs) occur from the initial moments where T(el) is still not definable. Our study shows that ultrafast-and-efficient phonon generations occur beyond the TTM scheme, presumably associated to the long duration of the non-thermal electrons in graphite.