The collisions between Na atoms and H2 molecules are of great significance in the field of chemical reaction dynamics, but the corresponding dynamics results of ground-state reactions have not been reported experimentally or theoretically. Herein, a global and high-precision potential energy surface (PES) of NaH2 (12A′) is constructed by the neural network model based on 21,873 high-level ab initio points. On the newly constructed PES, the quantum dynamics calculations on the Na(2S) + H2(v0 = 0, j0 = 0) → NaH + H reaction are carried out using the time-dependent wave packet method to study the microscopic reaction mechanism at the state-to-state level. The calculated results show that the low-vibrational products are mainly formed by the dissociation of the triatomic complex; whereas, the direct reaction process dominates the generation of the products with high-vibrational states. The reaction generally follows the direct H-abstraction process, and there is also the short-lived complex-forming mechanism that occurs when the collision energy exceeds the reaction threshold slightly. The PES could be used to further study the stereodynamics effects of isotope substitution and rovibrational excitations on the title reaction, and the presented dynamics data would provide an important reference on the corresponding experimental research at a higher level.