The square matrix-based convergence map (CM) method has proven effective in characterizing nonlinear dynamics in several 4-D dynamical systems. However, when time-dependent perturbations, such as crabbing kicks in colliders, are present, a comprehensive 6-D analysis becomes essential to accurately capture the coupling between transverse and longitudinal motions. In this work, we extend the CM method to the full 6-D phase space by employing an eigen-decomposition-based formulation of the square matrix combined with iterative procedures. The proposed 6-D CM approach is first validated using a simplified crabbing map and subsequently applied to the dynamic aperture (DA) study of the future Electron-Ion Collider (EIC). The CM results show qualitative consistency with frequency analysis in identifying major resonance structures and stability boundaries by using only one-turn map, suggesting that the 6-D CM can serve as a fast indicator for nonlinear beam dynamics analysis.