Contrary to typical layman belief, marine deposits on or near a continental shelf are not commonly formed by slow, gradual, consistent sedimentation from near the surface from soil particles derived from river deltas or continental runoff (terrigenous) or from organic byproducts (i.e. coccolithophorids - planktonic algae - debris that forms part of chalk, i.e. biogenetic ooze). Much of the sedimentation and the geologic features are created by deposition by massive debris flows, turbidity currents, and slumps (slope failures). These are in addition to overall "fan" valley and channel complex features from currents originating from the river sources. A conceptual image of a rapid debris flow and turbidity current (by Mike Clark) is provided below. Debris flows can be hundreds of meters high and move as rapid as 30 mph. Turbidity currents, debris flows, and slope failures can also be instigated by earthquakes and volcanic activity.
Erosion features are also commonly formed by high velocity underwater flows and include gulleys on the upper continental slope (tens of meters to hundreds of meters deep!) and canyons several km wide and hundreds of meters deep. Sub-marine fans can be a few km to several thousand km wide.
Large thicknesses of sedimentation therefore occur in marine environments near continental shelves or submarine volcanoes and mountain ranges within a matter of minutes, hours, and days, and not "millions of years".
Rapid deposition by debris flows, slumps, and sediment dense turbidity flows will cause rapid burial of organisms (plant and animal life) and permit fossilization.
Sub-marine geology and sedimentation is highly complex as discovered by advanced studies performed with every passing year. More and more literature is available describing these processes and there is still much to be learned because much is still hypothesized (i.e. debate over coarse turbidity deposits).