Nonequilibrium Green’s functions provide an efficient way to describe the evolution of the energy-momentum tensor during the early-time preequilibrium stage of high-energy heavy-ion collisions. Besides their practical relevance they also provide a meaningful way to address the question when and to what extent a hydrodynamic description of the system becomes applicable. Within the kinetic theory framework we derive a new method to calculate time-dependent nonequilibrium Green’s functions describing the evolution of energy and momentum perturbations on top of an evolving far-from-equilibrium background. We discuss the approach toward viscous hydrodynamics along with the emergence of various scaling phenomena for conformal systems. By comparing our results obtained in the relaxation time approximation to previous calculations in Yang-Mills kinetic theory, we further address the question which macroscopic features of the energy-momentum tensor are sensitive to the underlying microscopic dynamics.