We have developed a new data-driven method to solve the free-surface-related multiple problem using forward space-time-domain modeling. We build a finite-difference (FD) modeling engine in which the interaction of any desired wavefield with an unknown subsurface (but without the reflecting sea surface on top) can be modeled. This can either be used to predict the desired primary reflections of the subsurface or to (simultaneously) model all orders of free-surface-related multiples. In this method, we use conventional forward-modeling techniques in combination with a novel type of boundary condition. The wave propagation in the known part of the medium (i.e., the homogeneous water layer) is modeled on an FD grid, whereas the wave propagation in the unknown part of the medium (i.e., the subsurface) is predicted using the recorded multicomponent data. The methodology dynamically links these two distinct domains. We demonstrate the exact method and an adapted version that works under realistic conditions on a synthetic data set for different acquisition geometries. A small-scale test on ocean-bottom cable field data shows that the proposed method readily predicted the expected multiple arrivals in the recorded data.