We discuss the onset of the thermalization process in high-energy heavy-ion collisions from a weak coupling perspective, using classical-statistical real-time lattice simulations as a first principles tool to study the pre-equilibrium dynamics. Most remarkably, we find that the thermalization process is governed by a universal attractor, where the space-time evolution of the plasma becomes independent of the initial conditions and exhibits the self-similar dynamics characteristic of wave turbulence. We discuss the consequences of our weak coupling results for the thermalization process in heavy-ion experiments and briefly comment on the use of weak coupling techniques at larger values of the coupling.