In recent years, hydrogen (H2) has become the most sought-after sustainable energy carrier by virtue of its high energy content and carbon-free emission. The practical implementation of hydrogen as an alternative fuel calls for an efficient and secure storage medium. Within this framework, we have investigated Li-grafted Si-doped γ-graphyne for H2 storage applications by implementing the cutting-edge density functional theory (DFT). A dynamically and thermally stable Si-doped γ-graphyne (SiG) monolayer is functionalized with Li metal atoms that augmented the hydrogen binding strength of the nanolayer by almost three times, owing to the polarization effect of the Li atoms. The Li metal atoms get adsorbed over the monolayer, allowing a binding energy of -2.73 eV that is greater than the Li cohesive energy (-1.63 eV), which eliminates the metal-metal clustering probability. The reliability of the Li-functionalized SiG monolayer (Li8SiG) at elevated temperature has been further substantiated by performing and analyzing ab initio molecular dynamics (AIMD) simulations at 400 K. It is noteworthy that a total of four H2 molecules are held up by each Li atom with an average adsorption energy of -0.32 eV and a maximum gravimetric capacity of 8.48 wt%, which remarkably follows the US-DOE parameters. Partial density of states and Hirshfeld charge analysis are utilized to recognize the interaction channel which reveals the Kubas and Niu-Rao-Jena-like bonding among the metal atoms and loaded hydrogen molecules. The hydrogen occupancy calculated at different temperatures and pressures indicates that hydrogen molecules can be reversibly stored over the Li8SiG system, and it is noted that adsorbed H2 begins to desorb at 280 K, with complete desorption at 400 K and 20 atm (or lower). AIMD simulations are further performed to authenticate the H2 desorption at various temperatures, which agrees well with the occupation number analysis. All the outcomes advocate for efficient reversible hydrogen storage over the proposed host material.