Surprisingly the Persian Gulf is likely the exact opposite scenario. Modern research suggests that ancient likes like Ur were likely on the coastline while modern Basra would have been totally submerged. In most of the world the post glacial trend has pushed the coastline in but in the Persian gulf the trend points the other way. There is the possibility that the reason that Iraq is such a gold mine for archeological sites is because it is one of the rare places where the sea went the other way.
I think we are undercounting how much silt gets deposited by major river systems over millenia. The ruins of Lothal, which was a Harappan port city contemporary with Ur are pretty far inland as well. Who knows? Maybe Giza was closer to the coast and was part of a major Nilotic coastal metropolis
