The proposals merited just two sentences in Governor Andrew M. Cuomo’s State of the State speech on Wednesday, but if they came to pass they could mean a dramatic makeover of Brooklyn’s Red Hook neighborhood, and its stretch of still-industrial waterfront.

The idea would be to extend the subway from Lower Manhattan to the neighborhood, using a tunnel underneath the East River. The container terminal along the shoreline would be relocated to Sunset Park, potentially clearing the way for the redevelopment of more than 130 acres of publicly owned waterfront.

With a new subway stop with direct access to Manhattan, the now relatively isolated Red Hook could draw thousands of low-income, working-class and middle-class residents to affordable apartments that would be part of the development, a priority of both Mr. Cuomo and Mayor Bill de Blasio.

The scale is staggering. The potential redevelopment area is larger than Battery Park City, the community built on landfill in Lower Manhattan, and about six times as big as the largest private real estate development in the United States: the $25 billion Hudson Yards complex now taking shape on the Far West Side of Manhattan.