In the latest experimental success in the field of two-dimensional materials, ZnIn2S4 nanosheets with a highly appealing efficiency for photocatalytic hydrogen evolution were synthesized [S. Zhang, ACS Nano 15, 15238 (2021)1936-085110.1021/acsnano.1c05834]. Motivated by this accomplishment, herein, we conduct first-principles-based calculations to explore the physical properties of the ZnIn2X4 (X = S, Se, Te) monolayers. The results confirm the desirable dynamical and mechanical stability of the ZnIn2X4 monolayers. ZnIn2S4 and ZnIn2Se4 are semiconductors with direct band gaps of 3.94 and 2.77 eV, respectively while ZnIn2Te4 shows an indirect band gap of 1.84 eV. The optical properties achieved from the solution of the Bethe-Salpeter equation predict the exciton binding energy of the ZnIn2S4, ZnIn2Se4, and ZnIn2Te4 monolayers to be 0.51, 0.41, and 0.34 eV, respectively, suggesting the high stability of the excitonic states against thermal dissociation. Using the iterative solutions of the Boltzmann transport equation accelerated by machine learning interatomic potentials, the room-temperature lattice thermal conductivity of the ZnIn2S4, ZnIn2Se4, and ZnIn2Te4 monolayers is predicted to be remarkably low as 5.8, 2.0, and 0.4 W/mK, respectively. Due to the low lattice thermal conductivity, high thermopower, and large figure of merit, we propose the ZnIn2Se4 and ZnIn2Te4 monolayers as promising candidates for thermoelectric energy conversion systems. This study provides an extensive vision concerning the intrinsic physical properties of the ZnIn2X4 nanosheets and highlights their characteristics for energy conversion and optoelectronics applications.