Continental breakup is a fundamental tectonic process, which leads to seafloor spreading and the generation of oceanic crust. However, the current understanding of continental margins, based largely on 2‐D seismic transects, is inadequate to capture the spatial complexity of crustal evolution. Here we present a 3‐D seismic velocity model through a young, magma‐poor margin at the north‐eastern Gulf of Aden. Our results highlight the 45° obliquity between the strike of crustal thinning and extension direction, which is accommodated by two transfer zones during the formation of the Continent‐Ocean Transition (COT). This obliquity causes the margin to be segmented, which predates seafloor spreading. Along strike, we find a progressive eastward crustal thinning from 13 to 5 km, corresponding to a V‐shaped COT. This eastward variation is characterized by (a) an eastward increase of mantle exhumation due to detachment faulting, and (b) post‐rift magmatism emplaced onto serpentinized mantle in the west.