Electron-boson scattering that is peaked in the forward direction has been suggested as an essential ingredient for enhanced superconductivity observed in FeSe monolayers. Here, we study the superconducting state of a system dominated by forward scattering in the time-domain and contrast its behavior against the standard isotropic BCS case for both s- and d-wave symmetries. An analysis of the electron's dynamics in the pump-driven non-equilibrium state reveals that the superconducting order in the forward-focused case is robust and persistent against the pump-induced perturbations. The superconducting order parameter also exhibits a non-uniform melting in momentum space. We show that this behavior is in sharp contrast to the isotropic interaction case and propose that time-resolved approaches are a potentially powerful tool to differentiate the nature of the dominant coupling in correlated materials.