Hurricanes and coastal floods are among the most disastrous natural hazards. Both are intimately related to storm surges, as their causes and effects, respectively. However, the short-term forecasting of storm surges has proven challenging, especially when targeting previously unseen locations or sites without tidal gauges. Furthermore, recent work improved short and medium-term weather forecasting but the handling of raw unassimilated data remains non-trivial. In this paper, we tackle both challenges and demonstrate that neural networks can implicitly assimilate sparse in situ tide gauge data with coarse ocean state reanalysis in order to forecast storm surges. We curate a global dataset to learn and validate the dense prediction of storm surges, building on preceding efforts. Other than prior work limited to known gauges, our approach extends to ungauged sites, paving the way for global storm surge forecasting.