  We show that a dark Higgs field charged under U(1)$_{\rm H}$ gauge symmetry
is trapped at the origin for a long time, if dark photons are produced by an
axion condensate via tachyonic preheating. The trapped dark Higgs can drive
late-time inflation, producing a large amount of entropy. Unlike thermal
inflation, the dark Higgs potential does not have to be very flat, because the
effective mass for the dark Higgs is enhanced by large field values of dark
photons with extremely low momentum. After inflation, the dark Higgs decays
into massive dark photons, which further decay into the SM particles through a
kinetic mixing. We show that a large portion of the viable parameter space is
within the future experimental searches for the dark photon, because the
kinetic mixing is bounded below for successful reheating. We also comment on
the Schwinger effect which can hamper the tachyonic production of dark photons,
when the mass of dark photon is not the St\"{u}ckelberg mass, but is generated
by the Higgs mechanism. Such non-thermal trapped inflation could be applied to
other cosmological scenarios such as the early dark energy, known as one of the
solutions to the Hubble tension.
