Topological insulators are centered on the objective that a spin-locked surface state exhibits exceptional spin transport properties with an insulating bulk. In the present work, we predict biaxial strain-induced topological phase transition in the noncentrosymmetric compound AgCaAs, using first-principles calculations. Under ambient conditions, bulk AgCaAs exhibits a trivial nature with an insulating gap; however, on applying biaxial strain the system exhibits Dirac semimetallic behavior, indicating toward topological phase transition. At a 2% biaxial strain, a non-trivial topological phase emerges, which is verified by the orbital inversion across the Fermi level with a massless Dirac cone along the surfaces. Furthermore, by confining the bulk system in one dimension, we obtained a 2D AgCaAs (1T-MoS 2 type) system. The low-dimensional phase exhibits a trivial nature having a 0.48 eV energy gap. Under a moderate tensile strain, the system undergoes a topological phase transition with a 26.2 meV non-trivial energy gap. Such spin−orbit coupling-induced topological phase transition is further confirmed by computing and analyzing the 2 invariants, surface states, slab band structure, and evolution of Wannier charge centers. In terms of energy application, 2D AgCaAs exhibits excellent catalytic activity toward hydrogen evolution reactions. Investigating the catalytic properties of 2D AgCaAs in their non-trivial state has become a pathway for topological quantum catalysis. The Gibbs free energy for 2D AgCaAs was found to be −0.13 eV and suggests an opportunity for experimentalists to develop a catalyst for energy applications. Our findings deliver new insights into next-generation nano-electronics and better catalysts.