We present a theory of evolution of wind waves in time and space under abruptly applied wind forcing that is experimentally validated in a laboratory wind-wave tank. The model describes qualitatively and quantitatively the complex wave field development from the initial smooth surface to the finite state. The stochastic nature of wind waves is treated by considering an ensemble of coexisting unstable harmonics that grow due to shear flow instability. Breaking limits the wave growth initially; the process is then controlled by fetch-limited growth duration.