Hybrid aluminum matrix composites (HAMCs) are a new class of advanced composite and hybrid materials that can be customized and engineered to achieve specific properties for specific applications in specific environments. HAMCs are popular in the transportation industry due to their reduced cost and fuel consumption as compared to conventional materials. This research article has mainly focused on multi-response optimization through an L16 orthogonal array experimental design employing Taguchi-based Grey Relational Analysis. It was intended to explore the influence of tetra hybrid reinforced HAMCs synthesized using pure Al matrix with fixed wt% of primary reinforcements (5 wt% SiC and 5 wt% Al2O3) and varying wt% of secondary reinforcements such as (0.5, 2.5, 4.5, and 6.5) wt% of Gr and (0.5, 2.5, 4.5, and 6.5) wt% of SCBA on physicomechanical properties of HAMCs when milling time, compaction pressure, and sintering temperature were varied. The Taguchi-Grey’s relational analysis gave the optimal combination of the process and reinforcement parameters for both the physical and the mechanical properties such as milling time (5 h.), compaction pressure (55 MPa), sintering temperature (450 °C), Gr content (0.5 wt%), and SCBA content (4.5 wt%). At the optimum parameter settings, the average density, porosity, hardness, compressive strength, and ultimate tensile strength were 2.5118 gm cm−3, 0.8653%, 4228.45 MPa, 343.33 MPa, and 1516.41 MPa, respectively. The utilization of Taguchi and GRA methods have significantly confirmed that the influence of compaction pressure was highest among the all the other four parameters. The newly synthesized tetra hybrid reinforced HAMCs have shown superior physicomechanical properties compared to pure Al, and single as well as double reinforced HAMCs. Therefore, it is anticipated that the newly developed tetra hybrid reinforced AMC material will be utilized in heavy-duty, aerospace, medical, automotive, marine, and other applications.