Three-dimensional seismic interpretation of Tertiary sills within the northeast Atlantic margin demonstrates that shallow-level (<1 km) intrusion of igneous sills below the seafloor can deform the interface between water and sediment during its early burial stage by hydraulic elevation of the overburden. We show that a group of interconnected sills forcibly “jacked up” the seafloor, contributing to the creation of a minibasin 5 km wide, 250 m deep, and >20 km long. The fill of the minibasin is dated biostratigraphically as 54.6–55 Ma, which fits well with radiometric dates for the timing of intrusion of sills around this basin (ca. 53–55 Ma). The recognition and dating of onlap-fill seismic reflector packages that are delimited by forced folds form a new and useful method for dating shallow-level igneous intrusions in sedimentary basins, a method that provides independent constraints on radiometric dating techniques. Similar forced folds are recognized from other basins that have shallow-level sills, suggesting that the technique presented here may be similarly applicable in comparable geologic settings.