A deep learning (DL) model, based on a transformer architecture, is trained on a climate-model dataset and compared with a standard linear inverse model (LIM) in the tropical Pacific. We show that the DL model produces more accurate forecasts compared to the LIM when tested on a reanalysis dataset. We then assess the ability of an ensemble Kalman filter to reconstruct the monthly-averaged upper ocean from a noisy set of 24 sea-surface temperature observations designed to mimic existing coral proxy measurements, and compare results for the DL model and LIM. Due to signal damping in the DL model, we implement a novel inflation technique by adding noise from hindcast experiments. Results show that assimilating observations with the DL model yields better reconstructions than the LIM for observation averaging times ranging from one month to one year. The improved reconstruction is due to the enhanced predictive capabilities of the DL model, which map the memory of past observations to future assimilation times.