The mechanical, optoelectronic, and thermodynamic properties of carbon silicon nitride spinel compound have been investigated using density functional theory. The exchange-correlation potential was treated with the local density approximation (LDA) and the generalized gradient approximation of Perdew-Burke and Ernzerhof (PBE-GGA). In addition, the Engel-Vosko generalized gradient approximation (EV-GGA) and the modified Becke-Johnson potential (TB-mBJ) were also applied to improve the electronic band structure calculations. The ground state properties, including lattice constants and bulk modulus, are in fairly good agreement with the available theoretical data. The elastic constants, Young's modulus, shear modulus, and Poisson's ratio have been determined by using the variation of the total energy with strain. From the elastic parameters, it is inferred that this compound is brittle in nature. The results of the electronic band structure show that CSi2N4 has a direct energy band gap (I"-I"). The TB-mBJ approximation yields larger fundamental band gaps compared to those of LDA, PBE-GGA, and EV-GGA. In addition, we have calculated the optical properties, namely, the real and the imaginary parts of the dielectric function, refractive index, extinction coefficient, reflectivity, and energy loss function for radiation up to 40.0 eV. Using the quasi-harmonic Debye model which considers the phononic effects, the effect of pressure P and temperature T on the lattice parameter, bulk modulus, thermal expansion coefficient, Debye temperature, and the heat capacity for this compound were investigated for the first time.