This study presents a comprehensive investigation of the electronic, mechanical, and thermodynamic properties of Zintl phase hydrides XGaSiH (X = Sr, Ca, Ba) using Density Functional Theory (DFT) and the FP-LAPW method within the WIEN2k package. Our analysis covers the structural stability, electronic properties, and hydrogen interaction mechanisms in these compounds. The hydrides exhibit narrow band gaps, with values ranging from 0.1 to 0.5 eV using GGA and LDA functionals, and 0.6–1.0 eV with mBJ-GGA and mBJ-LDA. The hydrogen storage capacities are determined to be 0.34 wt %, 0.47 wt %, and 0.40 wt % for SrGaSiH, CaGaSiH, and BaGaSiH, respectively, highlighting their potential for energy storage applications. Thermodynamic properties, evaluated through the quasi-harmonic Debye model, provide insights into the Grüneisen parameter, heat capacity, and thermal expansion coefficient over a range of pressures (0–50 GPa) and temperatures (up to 1000 K). Elastic constants reveal that these compounds are mechanically stable, with a notable anisotropy in the {100} plane and varying degrees of compressibility among the different hydrides. Our study further highlights the slightly ordered hexagonal Ga and Si layers, which contribute to the enhanced hydrogen storage capabilities of these materials. The compounds demonstrate high structural stability, facilitating effective hydrogen retention and release at practical temperatures, making them promising candidates for hydrogen storage applications. Additionally, the analysis of electronic band structures and density of states suggests significant conductivity potential, with band gaps ranging from 0.1 to 1.0 eV, depending on the computational method used. The unique combination of structural, electronic, thermodynamic, and mechanical properties in XGaSiH compounds positions them as valuable materials for renewable energy applications. These findings lay the groundwork for future research focused on optimizing these materials through structural modifications or doping to enhance performance metrics such as hydrogen storage capacity and electrical conductivity.