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(k(x),k(y);t) and find that the k(x)=0 component exhibits dynamic scaling, of the form S(0,k(y);t)=t(beta)S(k(y)t(alpha)). Over a significant range of times, we observe excellent data collapse with alpha=1/2 and beta=1. The effects of varying filling fraction and driving force are discussed.