We present a Bayesian inference of the equation of state (EOS) of cold, dense matter within a density-dependent relativistic mean-field (DD-RMF) model. To connect macroscopic nuclear-matter properties to microscopic interaction channels in a reproducible way, we employ an explicit inverse-mapping procedure that constructs the density-dependent couplings from a physically interpretable 10-dimensional parameter set, while enforcing thermodynamic consistency and applying stability and causality filters. The reconstructed EOS is confronted with complementary multi-messenger constraints: low-density chiral effective field theory ($\chi$EFT) bands, intermediate-density heavy-ion collision (HIC) flow information, NICER mass--radius posteriors, and the existence of $\sim 2\,M_\odot$ pulsars. We find that the combined dataset strongly restricts both isovector and isoscalar sectors. In particular, the $\chi$EFT band favors a relatively soft symmetry-energy slope, $L\simeq 38~\mathrm{MeV}$, which correlates with a compact canonical radius $R_{1.4}\simeq 11.6~\mathrm{km}$. To simultaneously reproduce the intermediate-density softness indicated by HIC constraints and the high-density stiffness required by heavy pulsars, the posterior favors a moderately large Dirac effective mass at saturation ($M^*/M\simeq 0.64$) together with correlated, non-vanishing high-density limits of the scalar and vector couplings. The inferred sound-speed profile remains causal and exhibits pronounced nonconformal stiffening, with $c_s^2$ exceeding $1/3$ around a few times saturation density ($n\sim 3n_0$), suggesting that matter in the cores of massive neutron stars is far from a scale-invariant conformal regime. Finally, evidence-based diagnostics yield strong overall compatibility (e.g., $\ln R\gtrsim 9$ for the combined NS+$\chi$EFT+HIC sectors) within the present DD-RMF model class and adopted priors, indicating that terrestrial and astrophysical constraints can be jointly accommodated in a unified description of the neutron-star EOS.