Fiber-reinforced polymer composites are widely used in lightweight engineering structures due to their high specific strength and stiffness. However, their performance under concentrated out-of-plane loading is strongly dependent on the distribution and arrangement of fibers through the thickness. In this study, the quasi-static impact behavior of glass/polyester hybrid composites was investigated, with particular emphasis on the effect of fiber distribution across the thickness. For this purpose, pure glass, inter-ply, intra-ply, and three functionally graded material (FGM) configurations with different patterns of arrangement in the volume fractions of glass and polyester fibers were fabricated and experimentally tested. The resulting force-displacement curves were analyzed to evaluate the mechanical parameters, and the surface damage of the specimens was examined after testing. The results demonstrated that altering the fiber arrangement not only changes the stiffness and load-bearing capacity but also significantly affects the overall load-carrying mechanism and the manner in which structural capacity deteriorates after damage initiation. Among the investigated configurations, FGM1 and FGM2 absorbed 109 and 116 J of energy, respectively, while maintaining a maximum load at or above that of the pure glass, which absorbed 63 J. FGM2 exhibited the most balanced overall response, simultaneously achieving an initial stiffness of 852 N/mm, a peak load of 8538 N, a displacement of 11.63 mm, and the highest energy absorption. These findings demonstrate that controlling the gradual distribution of fibers through the thickness can enhance the deformation capacity and energy absorption of composite materials without a significant reduction in load-bearing capacity, while also mitigating the rapid loss of load-carrying capacity following damage propagation.