Sea-level rise (SLR) poses risks to millions of people worldwide. Although these risks are partially driven by anthropogenic CO2 emissions, the relative contribution of uncertain societal choices (e.g. decarbonization) and Earth-system dynamics (e.g. Antarctic Ice Sheet (AIS) tipping points) on future sea-level projections is poorly understood. This is in part due to a reliance on a handful of non-probabilistic and non-representative emissions scenarios, which are difficult to integrate with geophysical uncertainties. Here, we use a chained model framework to disentangle the relative impacts of these uncertainties on projected global mean sea levels. The emissions trajectory, particularly the timing of when emissions are reduced, becomes the primary driver of sea-level variability prior to 2100. Even under relatively optimistic assumptions about future emissions trajectories, there is a moderate probability of triggering AIS marine ice instabilities, resulting in high-end SLR. We quantify how delaying decarbonization by even a few decades can reduce the “safe operating space” associated with the geophysical uncertainties. Our results highlight the potential for rapid mitigation of CO2 emissions to reduce, but not eliminate, high-end SLR. However, the window to avoid future high-end SLR is closing and requires emissions to decrease rapidly and soon.