We investigate the $1S$-, $1P$-, $2S$-, and $1D$-wave ${\Omega }_c(css)$ spectroscopy through the non-leptonic decays of ${\Omega }_b^{-}$ baryon within the constituent quark model. For the lowest-lying $1S$-wave ${\Omega }_c$ state, we obtain the branching fractions ${\cal B}(\Omega_b^- \to \Omega_c^0 \pi^-,\Omega_c^0 \rho^-)=(0.98^{+0.24+0.73}_{-0.11-0.56}, 5.33^{+1.31+3.74}_{-0.60-2.93}) \times 10^{-3}$, which are consistent with existing model predictions. For ${\Omega }_c(3000)$, ${\Omega }_c(3050)$, ${\Omega }_c(3065)$, and ${\Omega }_c(3090)$, observed in the proton-proton and $e^{+}{e}^{-}$ collisions and interpreted as members of the $1P$-wave multiplet (collectively denoted as ${\Omega }_c^{**}$), we predict the branching fractions of ${\Omega }_b^{-}\to {\Omega }_c^{**}{\pi }^{-},{\Omega }_c^{**}{\rho }^{-}$ at the level of ${10}^{-3}$. Assigning the newly observed ${\Omega }_c(3327)$ baryon to a $1D$-wave excitation with $J^P=5/2^{+}$ or $7/2^{+}$, we obtain ${\cal B}[\Omega_b^-\to \Omega_c(3327)^0\pi^-,\Omega_c(3327)^0\rho^-] =(1.19^{+0.29+0.39}_{-0.13-0.35},5.13^{+1.26+1.70}_{-0.58-1.48})\times 10^{-3}$ or $({3.77}_{-0.43-1.09}^{+0.93+1.25},{0.65}_{-0.07-0.18}^{+0.16+0.22})\times {10}^{-3}$, respectively. The pronounced differences between these two scenarios provide a clear discriminant that can be tested in future measurements at LHCb.