We present a statistical simulation method for the early stage of thin-film growth from vapor-deposited atoms, which simulate evolution of density, size, and spatial distribution of the growing islands on a supported substrate. The method describes surface processes of the deposited atoms by random walks and the Arrhenius form. However, we utilize the statistical behavior of the atomic surface processes over a time scale significantly larger than the typical attempt time (10-13 s). This novel method saves enormous simulation time and thus overcomes the difficulty resulting from the remarkable gap between the typical experimental deposition rates and the attempt frequency. The statistical approach is verified by comparisons with direct step-by-step (kinetic Monte Carlo) simulations at large deposition rates. Results obtained for low deposition rates matching experimental conditions are also presented.