  We demonstrate that dynamical probes provide direct means of detecting the
topological phase transition (TPT) between conventional and topological phases,
which would otherwise be difficult to access because of loss or heating
processes. We propose to avoid such heating by rapidly quenching in and out of
the short-lived topological phase across the transition that supports gapless
excitations. Following the quench, the distribution of excitations in the final
conventional phase carries signatures of the TPT. We apply this strategy to
study the TPT into a Majorana-carrying topological phase predicted in
one-dimensional spin-orbit-coupled Fermi gases with attractive interactions.
The resulting spin-resolved momentum distribution, computed by
self-consistently solving the time-dependent Bogoliubov--de Gennes equations,
exhibits Kibble-Zurek scaling and St\"{u}ckelberg oscillations characteristic
of the TPT. We discuss parameter regimes where the TPT is experimentally
accessible.
