Preheat oven to 350°.
Spray a Bundt pan with cooking spray. Pour dulce de leche in the bottom of the pan and use a brush to spread it up the sides of the pan.
Prepare the cake mix according to the box directions (usually requiring the ½ cup vegetable oil, 1 cup of water, and 3 eggs listed in the ingredients). Pour prepared batter on top of the caramel sauce.
Mix cream cheese, evaporated milk, sweetened condensed milk, 4 eggs, vanilla, and salt in a blender until smooth. Pour custard mixture through a strainer into the Bundt pan. It may appear to mix a bit—this is OK because it’ll separate when it cooks. Fit Bundt pan in a large pot and place in the oven. Pour boiling water into the pot so it is about ⅔ up the sides of the Bundt pan. Bake until the cake rises to the top and a toothpick inserted into the cake comes out clean, about 60–70 minutes.
Remove the Bundt pan from the water bath and cool on a rack for at least an hour. This cake can be made a day in advance and refrigerated until serving. To serve, flip the cake onto a plate. If any caramel sauce remains in the Bundt pan, simply heat it over the stove and pour over the top of the cake.