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We use a numerical solution of the deterministic time-dependent Ginzburg-Landau (TDGL) equations to determine the response induced by a probe field in a material quenched into a superconducting state. We characterize differences in response according to whether the probe is applied before, during, or after the phase stiffness has built up to its final steady-state value. We put an emphasis on the extent to which superfluid response requires a non-negligible phase stiffness, which for the considered quench has to build up dynamically. A key finding is that the time-dependent phase stiffness controls the likelihood of phase slips as well as the magnitude of the electromagnetic response. Additionally, we address the electromagnetic response expected if the probe itself is strong enough to activate phase slip processes. If the probe is applied before phase stiffness is sufficiently built up, we find that phase slips occur so that the vector potential is compensated and no long-term supercurrent is induced, while if it is applied at sufficient phase stiffness a weak probe pulse will induce a state with a long-lived supercurrent. If the probe is strong enough to activate the phase slip process, the supercurrent state will only be metastable with a lifetime that scales logarithmically with the amplitude of fluctuations in the magnitude of the order parameter. Finally, we study the response to experimentally motivated probe fields (electric field that integrates to zero). Interestingly, depending on the relative time difference of the probe field to the buildup of superconductivity, long-lived supercurrents can be induced even though the net change in vector potential is zero. [ABSTRACT FROM AUTHOR]