The mixing of ocean waters on continental shelves, which is mainly driven by waves, tides, and currents, plays a key role in the physics, biogeochemistry, and ecology of coastal regions. This study focuses on four months of continuous data recorded along a telecommunication cable offshore Oregon, USA, with Distributed Acoustic Sensing (DAS). We apply a cross-correlation approach to the continuous DAS data to infer the propagation of ocean surface gravity waves in the 3 to 100 s period range and estimate near-surface ocean flows. We observe strong spatio-temporal variations of ocean flows along the cable over four months, with strong impacts from a series of storms in late October 2021. We find that our measurements capture oceanic surface motions as those measured by nearby traditional oceanographic instruments. This study demonstrates that ocean-bottom DAS can be used to infer the dynamic properties of near-shore oceans with an unprecedented spatio-temporal resolution.