We develop a macroscopic description of the space-time evolution of the energy-momentum tensor during the pre-equilibrium stage of a high-energy heavy-ion collision. Based on a weak coupling effective kinetic description of the microscopic equilibration process (`a la bottom-up), we calculate the non-equilibrium evolution of the local background energy-momentum tensor as well as the non-equilibrium linear response to transverse energy and momentum perturbations for realistic boost-invariant initial conditions for heavy ion collisions. We demonstrate how this framework can be used on an event-by-event basis to propagate the energy momentum tensor from far-from-equilibrium initial state models, e.g. IP-Glasma, to the time $tau_text{hydro}$ when the system is well described by relativistic viscous hydrodynamics. The subsequent hydrodynamic evolution becomes essentially independent of the hydrodynamic initialization time $tau_text{hydro}$ as long as $tau_text{hydro}$ is chosen in an appropriate range where both kinetic and hydrodynamic descriptions overlap. We find that for $sqrt{s_{NN}}=2.76,text{TeV}$ central Pb-Pb collisions, the typical time scale when viscous hydrodynamics with shear viscosity over entropy ratio $eta/s=0.16$ becomes applicable is $tau_text{hydro}sim 1,text{fm/c}$ after the collision.
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