  Detecting dark matter (DM) relic via freeze-in is difficult in laboratories
due to smallness of the couplings involved. However, a non-standard
cosmological history of the Universe, prior to Big Bang Nucleosynthesis (BBN),
can dramatically change this scenario. In this context, we study the freeze-in
production of dark matter in classically scale invariant $U(1)_X$ gauge
extension of the Standard Model (SM), recently dubbed as the \textit{Scale
Invariant FIMP Miracle}. We assume an additional species dominates the energy
density of the Universe at early times, causing the expansion rate at a given
temperature to be larger than that in the standard radiation-dominated case. We
find, the \textit{out-of-equilibrium} scattering processes involving particles
in the thermal bath lead to significantly suppressed DM production in this era,
thereby enhancing the couplings between the visible and the dark sector (by
several orders of magnitude) to satisfy the observed DM abundance, and
improving the detection prospects for freeze-in in turn. Scale invariance of
the underlying theory leaves only four free parameters in the model: the DM
mass $m_X$, the gauge coupling $g_X$, the temperature of transition $T_R$ from
early scalar-dominated to radiation-dominated era and the power-law dependence
$n$ of this temperature. We show, within this minimal set-up, experiments like
FASER, MATHUSLA, DUNE, SHiP will be probing various cosmological models
depending on the choice of $\{n,\,T_R\}$ that also satisfy the PLANCK observed
relic density bound. Moreover, due to the presence of a naturally light scalar
mediator, the direct detection of the DM at XENON1T, PandaX-4T or XENONnT
becomes relevant for Higgs-scalar mixing $\sin\theta\simeq\{10^{-5}-10^{-3}\}$,
thus providing complementary probes for freeze-in, as well as for non-standard
cosmological pre-BBN era.
