The ground state structural, mechanical, electronic, vibrational, optical, and thermoelectric properties of the newly synthesized quaternary LiTiCoSn compound is deliberated elaborately with the help of ab-initio tactics formulated under the framework of density functional theory. The calculated results of equilibrium structural parameters are observed to be in fairly good agreement with the available similar theoretical as well as experimental data. Structural optimization has been done for three diverse crystal structure configurations that is, Type 1, Type 2, and Type 3. After studying optimization curves, it is found that Type 2 crystal structure is the most stable structure for this compound as it possesses the minimum energy. The structural stability of this compound has been explored using three different exchange correlation functions that is, PBE-GGA, WC-GGA, and PBE-sol GGA for better understanding. It is found from our studies that the inclusion of the electronic exchange-correlation through the newly developed Trans-Blaha modified Beck-Johnson potential (TB-mBJ) along with PBE-GGA expands the portrayal of the obtained electronic band plots. Insertion of TB-mBJ potential vintages an indirect energy gap (Γ–X) of 1.052 eV for the studied compound, which reveals its semiconducting nature. Also, the elastic constants ($C_{\mathit{ij}}$) and the associated elastic moduli confirm its stability in the cubic phase and demonstrate its brittle nature. Furthermore, spectral dependency of dielectric function, refractive index, extinction coefficient, absorption coefficient, reflectivity, energy loss function, and optical conductivity on incident electromagnetic radiations up to 8 eV are also studied. The maximum power factor for the studied LiTiCoSn compound is obtained as 7.35 mWm⁻¹ K⁻² at room temperature, which increases to 17.10 mWm⁻¹ K⁻² at 700 K and 22.50 mWm⁻¹ K⁻² at 1200 K, respectively. So LiTiCoSn can be a novel sort of intriguing thermoelectric material as well as it can be used in optoelectronic and energy harvesting devices.