A two-dimensional lattice gas of two species, driven in opposite directions by an external force, undergoes a jamming transition if the filling fraction is sufficiently high. Using Monte Carlo simulations, we investigate the growth of these jams (‘‘clouds’’), as the system approaches a nonequilibrium steady state from a disordered initial state. We monitor the dynamic structure factor S(kx,ky;t) and find that the kx=0 component exhibits dynamic scaling, of the form S(0,ky;t)=tβS̃ (kytα). Over a significant range of times, we observe excellent data collapse with α=1/2 and β=1. The effects of varying filling fraction and driving force are discussed.