The Surface Water and Ocean Topography (SWOT) mission provides two-dimensional sea surface height (SSH) observations at kilometer-scale resolution, extending satellite altimetry toward finescale ocean variability. Estimating surface currents from these observations remains difficult at submesoscales, where the flow is not strictly geostrophic and SSH contains contributions from both balanced and unbalanced motions. Internal tides and internal gravity waves further complicate the relationship between SSH and the balanced circulation, introducing ambiguity into conventional geostrophic retrievals. As a result, extracting the nonlinear, ageostrophic submesoscale dynamics from snapshot SSH data becomes inherently more difficult due to the underlying physics, calling for alternative approaches that can disentangle the competing contributions. We develop a physics-guided deep learning model to estimate balanced surface velocity from a single SSH snapshot. The model is trained using the tide-resolving LLC4320 simulation in the Kuroshio Extension, with the balanced and unbalanced components separated through a dynamical decomposition. Total SSH is used as input, and the corresponding balanced surface velocity is used as the supervised target. Extensive validation on independent LLC4320 samples shows that the proposed framework faithfully reconstructs the dominant spatial patterns of submesoscale balanced currents and preserves their finescale kinetic energy signatures. The trained model is then applied to SWOT Level‑3 SSH observations over the Kuroshio Extension. The resulting velocity fields reveal narrow jets, filamentary structures, and sharpened velocity gradients. By contrast, such features are either absent or heavily smoothed in conventional altimetry‑derived products. The results demonstrate that physics‑guided deep learning can effectively exploit the high‑resolution SSH information provided by SWOT and reduces the ambiguity caused by unbalanced SSH variability. The proposed framework provides a nonlinear remote‑sensing retrieval strategy that extracts dynamically meaningful current information from a single SWOT SSH snapshot, offering a new pathway for utilizing SWOT measurements to investigate submesoscale ocean circulation in energetic regions where direct velocity observations remain sparse.