  MoEDAL's Apparatus for Penetrating Particles (MAPP) Experiment is designed to
expand the search for new physics at the LHC, significantly extending the
physics program of the baseline MoEDAL Experiment. The Phase-1 MAPP detector
(MAPP-1) is currently undergoing installation at the LHC's UA83 gallery
adjacent to the LHCb/MoEDAL region at Interaction Point 8 and will begin
data-taking in early 2024. The focus of the MAPP experiment is on the quest for
new feebly interacting particles$\unicode{x2014}$avatars of new physics with
extremely small Standard Model couplings, such as minicharged particles (mCPs).
In this study, we present the results of a comprehensive analysis of MAPP-1's
sensitivity to mCPs arising in the canonical model involving the kinetic mixing
of a massless dark $U(1)$ gauge field with the Standard Model hypercharge gauge
field. We focus on several dominant production mechanisms of mCPs at the LHC
across the mass$\unicode{x2013}$mixing parameter space of interest to MAPP:
Drell$\unicode{x2013}$Yan pair production, direct decays of heavy quarkonia and
light vector mesons, and single Dalitz decays of pseudoscalar mesons. The
$95\%$ confidence level background-free sensitivity of MAPP-1 for mCPs produced
at the LHC's Run 3 and the HL-LHC through these mechanisms, along with
projected constraints on the minicharged strongly interacting dark matter
window, are reported. Our results indicate that MAPP-1 exhibits sensitivity to
sizable regions of unconstrained parameter space and can probe effective
charges as low as $8 \times 10^{-4}\:e$ and $6 \times 10^{-4}\:e$ for Run 3 and
the HL-LHC, respectively.
