The history of organismal evolution, seawater chemistry, and paleoclimate is recorded in layers of carbonate sedimentary rock. Meter-scale cyclic stacking patterns in these carbonates often are interpreted as representing sea level change. A reliable sedimentary proxy for eustasy would be profoundly useful for reconstructing paleoclimate, since sea level responds to changes in temperature and ice volume. However, the translation from water depth to carbonate layering has proven difficult, with recent surveys of modern shallow water platforms revealing little correlation between carbonate facies (i.e., grain size, sedimentary bed forms, ecology) and water depth. We train a convolutional neural network with satellite imagery and new field observations from a 3,000 km2 region northwest of Andros Island (Bahamas) to generate a facies map with 5 m resolution. Leveraging a newly-published bathymetry for the same region, we test the hypothesis that one can extract a signal of water depth change, not simply from individual facies, but from sequences of facies transitions analogous to vertically stacked carbonate strata. Our Hidden Markov Model (HMM) can distinguish relative sea level fall from random variability with ∼90% accuracy. Finally, since shallowing-upward patterns can result from local (autogenic) processes in addition to forced mechanisms such as eustasy, we search for statistical tools to diagnose the presence or absence of external forcings on relative sea level. With a new data-driven forward model that simulates how modern facies mosaics evolve to stack strata, we show how different sea level forcings generate characteristic patterns of cycle thicknesses in shallow carbonates, providing a new tool for quantitative reconstruction of ancient sea level conditions from the geologic record.