We study time-resolved charge transport in a superconducting nanowire using time-dependent Landauer–Büttiker theory. We find that the steady-state Majorana zero-bias conductance peak emerges transiently accompanied by characteristic oscillations after a bias-voltage quench. These oscillations are suppressed for trivial impurity states (IS) that otherwise show a similar steady-state signal as the Majorana zero mode (MZM). In addition, we find that Andreev bound states or quasi-Majorana states (QMS) in the topologically trivial bulk phase can give rise to a zero-bias conductance peak, also retaining the transient properties of the MZM. Our results imply that (1) time-resolved transport may be used as a probe to distinguish between the topological MZM and trivial IS; and (2) the QMS mimic the transient signatures of the topological MZMs.