While most ocean crust is formed from oceanic plate formations there are areas of the ocean (much of the Gulf of Mexico, Eastern US coast, North Sea, Arabian coast of India) which appear to be continental "land" for hundreds of miles before the shelf to the oceanic crust. How does this occur?
It's a geology question more than a geography question. These crusts are components of tectonic plates. Continental crust is less dense than oceanic crust, so it tends to ride higher than the denser oceanic crust. Typically the deeper parts of the world are oceanic crust and where the oceans are by virtue of water running downhill - thus the name. It's not named based on the presence or lack of water on top of it, but on the chemical composition of the rock that makes up the tectonic plate. So you can have exposed oceanic crust on like volcanic islands and submerged continental crust in the areas you described.
This is coming off from terrible memory from my geology undergrad like 15 odd years ago, FYI.
The reason why there are lands comprised of continental crust submerged far away from the coast is we are in an interglacial period inside the Pleistocene cycle.
There are extensive continental shelves that were formed during glacial periods when the sea level was lower.