  Extending the Higgs sector of the Standard Model (SM) by just one additional
Higgs doublet field leads to the two-Higgs-doublet model (2HDM). In the Type-I
$Z_2$-symmetric limit of the 2HDM, all the five new physical Higgs states can
be fairly light, $\mathcal{O}(100)$\,GeV or less, without being in conflict
with current data from the direct Higgs boson searches and the $B$-physics
measurements. In this article, we establish that the new neutral as well as the
charged Higgs bosons in this model can all be simultaneously observable in the
multi-$b$ final state. The statistical significance of the signature for each
of these Higgs states, resulting from the electro-weak (EW) production of their
pairs, can exceed 5$\sigma$ at the 13\,TeV High-Luminosity Large Hadron
Collider (HL-LHC). Since the parameter space configurations where this is
achievable are precluded in the other, more extensively pursued, 2HDM Types, an
experimental validation of our findings would be a clear indication that the
true underlying Higgs sector in nature is the Type-I 2HDM.
