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Although calcium carbonate (CaCO₃) precipitation plays an important role in nature, its mechanism remains only partially understood. Further understanding the atomic driving force behind the CaCO₃ precipitation could be key to facilitate the capture, immobilization, and utilization of CO₂ by mineralization. Here, based on molecular dynamics simulations, we investigate the mechanism of the early-stage nucleation of an amorphous calcium carbonate gel. We show that the gelation reaction manifests itself by the formation of some calcium carbonate clusters that grow over time. Interestingly, we demonstrate that the gelation reaction is driven by the existence of some competing local molecular stresses within the Ca and C precursors, which progressively get released upon gelation. This internal molecular stress is found to originate from the significantly different local coordination environments exhibited by Ca and C atoms. These results highlight the key role played by the local stress acting within the atomic network in governing gelation reactions.