The transient electric field governing the dynamics of space charge is investigated by time- and energy-resolved low-energy electron scattering. The space charge above a copper target is produced by high-intensity femtosecond laser pulses. The pump-probe experiment has a measured temporal resolution of better than 35 ps at 55 eV probe electron energy. The probe electron acceleration due to space charge is reproduced within a 3-dimensional non-relativistic model, which determines an effective number of electrons in the space charge cloud and its initial diameter. Comparison of the simulations with the experiments indicates a Coulomb explosion, which is consistent with transients in the order of 1 ns, the terminal kinetic energy of the cloud and the thermoemission currents predicted by the Richardson-Dushman formula.