We theoretically investigate the full time evolution of a nonequilibrium double quantum dot structure from initial conditions corresponding to different product states (no entanglement between dot and lead) to a nonequilibrium steady state. and an interaction-induced renormalization of energy levels. We find that when the system carries a single electron on average the formation of the steady state is strongly influenced by the coherence between the dots. The latter can be sizeable and indeed larger in the presence of a bias voltage than it is in equilibrium. Moreover, the interdot coherence is shown to lead to a pronounced difference in the population of the dots.