  We study the freeze-in production of vector dark matter (DM) in a classically
scale invariant theory, where the Standard Model (SM) is augmented with an
abelian $U(1)_X$ gauge symmetry that is spontaneously broken due to the
non-zero vacuum expectation value (VEV) of a scalar charged under the $U(1)_X$.
Generating the SM Higgs mass at 1-loop level, it leaves only two parameters in
the dark sector, namely, the DM mass $m_X$ and the gauge coupling $g_X$ as
independent, and supplement with a naturally light dark scalar particle. We
show, for $g_X\sim\mathcal{O}\left(10^{-5}\right)$, it is possible to produce
the DM X out-of-equilibrium in the early Universe, satisfying the observed
relic abundance for $m_X\sim\mathcal{O}\left(\text{TeV}\right)$, which in turn
also determines the scalar mixing angle $\sin
\theta\sim\mathcal{O}\left(10^{-5}\right)$. The presence of such naturally
light scalar mediator with tiny mixing with the SM, opens up the possibility
for the model to be explored in direct search experiment, which otherwise is
insensitive to standard freeze-in scenarios. Moreover we show that even with
such feeble couplings, necessary for the DM freeze-in, the scenario is testable
in several light dark sector searches (e.g., in DUNE and in FASER-II),
satisfying constraints from the observed relic abundance as well as big bang
nucleosynthesis (BBN). Particularly, we find, regions of the parameter space
with $m_X$ $\gtrsim 1.8$ TeV are insensitive to direct detection probes but
still can become accessible in lifetime frontier searches, courtesy to the
underlying scale invariance of the theory.
