Using high‐resolution seismic profiles and other geophysical data, collected during R/V Meteor Cruise M74/2, we investigate the distribution patterns of shallow sediments, their structure and deformation processes, and their role in the migration, accumulation and seepage of hydrocarbon‐rich fluids. Here, we show that rapid syn‐kinematic sedimentation at the frontal Makran accretionary prism provides a mechanism by which emerging imbricated thrust packets override the footwall at the seafloor without significant mass‐wasting and destruction of fault‐related anticline in the hanging wall. These anticlines may rise high above the seafloor to form plate‐boundary‐parallel ridges, and distinguish from simple thrust blocks seen at convergent margins elsewhere. With the fast burial of many thrust faults by the syn‐kinematic sediments, anticlinal growth structures form in these syn‐kinematic sediments by continuous thrust activity. The anticlinal structures preserved within the cores of the ridges or formed from these syn‐kinematic sediments act as structural traps for migrating hydrocarbon‐rich fluids, above which fluid escape structures are generated leading to seafloor seeps. Most of the discovered hydrocarbon seeps around Sixth Ridge are sourced from these traps. Despite the compressional environment and the rapid syn‐kinematic sedimentation rates, shallow subsurface of the frontal Makran is a normally pressured regime, in which the buoyancy of hydrocarbons may account for the fluid migration. In this important respect, the Makran accretionary prism differs from many other convergent margins and accretionary prisms, where fluid flow is largely driven by tectonically induced overpressure.