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How terrestrial ecosystems will accumulate carbon as the climate continues to change is a major source of uncertainty in projections of future climate. Under growth‐stimulating environmental change, time lags inherent in population and community dynamic processes have been posed to dampen, or alternatively amplify, short‐term carbon gain in terrestrial vegetation, but these outcomes can be difficult to predict. To theoretically frame this problem, we developed a simple model of vegetation dynamics that identifies the stage‐structured demographic and competitive processes that could govern the timescales of carbon storage and loss. We show that demographic lags associated with growth‐stimulating environmental change can allow a rapid increase in population‐level carbon storage that is lost back to the atmosphere in later years. However, this transient carbon storage only emerges when environmental change increases the transition of adult individuals into a larger size class that suffers markedly higher mortality. Otherwise, demographic lags simply slow carbon accumulation. Counterintuitively, an analogous tradeoff between maximum adult size and survivorship in two‐species models, coupled with environmental change‐driven replacement, does not generate the transient carbon gain seen in the single‐species models. Instead lags in competitive replacement slow the approach to the eventual carbon trajectory. Together, our results suggest that time lags inherent in demographic and compositional turnover tend to slow carbon accumulation in systems responding to growth‐stimulating environmental change. Only under specific conditions will lagged demographic processes in such systems drive transient carbon accumulation, conditions that investigators can examine in nature to help project future carbon trajectories. [ABSTRACT FROM AUTHOR]