We apply an intense infrared laser pulse in order to perturb the electronic and vibrational states in the three-dimensional charge density wave material 1$T$-VSe$_2$. Ultrafast snapshots of the light-induced hot carrier dynamics and non-equilibrium quasiparticle spectral function are collected using time- and angle-resolved photoemission spectroscopy. The hot carrier temperature and time-dependent electronic self-energy are extracted from the time-dependent spectral function, revealing that incoherent electron-phonon interactions heat the lattice above the charge density wave critical temperature on a timescale of $(200 pm 40)$~fs. Density functional perturbation theory calculations establish that the presence of hot carriers alters the overall phonon dispersion and quenches efficient low-energy acoustic phonon scattering channels, which results in a new quasi-equilibrium state that is experimentally observed.
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