We present a method for discovering temporal transitions in the macroscopic response of two granular assemblies of photoelastic disks, subject to prolonged symmetric cyclic pure shear - under uniform deformation. A distance-matrix- based analysis is used in a reconstructed state space formed from the macroscopic stress ratio time series, with the technique of quadrant scans applied to extract transition times from the recurrence plots. Macroscopic measures of pressure and shear stress exhibit limit cycle behavior with respect to the applied cyclic strain. The contact network and the strong force filamentary network, however, show a gradual change across shear cycles. A quantitative characterization of the self-organization process at the mesoscale reveals that the observed transition in system dynamics at the macroscale is consistent with the process of aging. A distinct and consistent pattern of self-organization with respect to the contact topology and the structural stability of force chains is uncovered. The contact topology evolves to a more densely connected and stable truss-laced lattice, embodying force chain columns endowed with higher levels of triangular and rectangular bracing. This results in an increase in the structural stability of force chains, consistent with the prevailing conjecture on the structural mechanism behind the observed increase in shear strength and shear stiffness in an aging sand.