Time crystals, with their intrinsic long-range temporal order and self-sustained oscillations, provide a unique platform for quantum applications that leverages long-lived coherence. We investigate the emergence of time-crystalline order in a continuously driven, dissipative atomic lattice featuring spatially inhomogeneous atom-atom interactions. The spatial dependence of these interactions spontaneously breaks the dynamical equivalence among lattice sites, resulting in the formation of distinct atomic subpopulations that exhibit unequal temporal responses. This spatially induced inequivalence lifts effective degeneracies within the driven system, thereby enabling the spontaneous breaking of continuous time-translation symmetry. As the driving strength is increased, the system undergoes a rich sequence of nonequilibrium dynamical regimes, including bistability, chaotic behavior, a stable time-crystalline phase, quasiperiodic dynamics, and ultimately an approach to a dynamical steady state. We further demonstrate that controlled initial inequivalence between atom ensembles significantly enhances the robustness of the time-crystalline phase. The interplay of detuning, interaction strength, and dissipation in either stabilizing or suppressing the emergent temporal order is systematically analyzed. This work suggests that spatial engineering of nonlinearities can serve as a design principle for generating temporal order within a mean-field description of driven quantum systems.

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• Spontaneous symmetry breaking
• Time crystals
• Dynamic critical phenomena
• Lindblad equation