In the collision of nuclei at high energies the produced matter reinteracts and forms a plasma which ultimately equilibrates and exhibits collective hydrodynamic flow. While a general theory of the equilibration process has been outlined previously, there were no practical frameworks to smoothly connect the early gluon production in classical field simulations with hydrodynamic simulations of the late time plasma expansion. We provide this practical tool (called KøMPøST) by constructing a set of non-equilibrium Green functions calculated in QCD kinetic theory. We demonstrate with a realistic simulation of a heavy ion collisions the smooth transition from the classical fields to hydrodynamics, and calculate the pragmatic lower bound on the system size for the hydrodynamics to be applicable.