Place sugar in a saucepan over medium heat. Cook, stirring frequently, until sugar melts into a golden caramel, about 10 minutes. Pour into a ring mold, tilting to coat the bottom evenly.
Pour condensed milk into a blender. Fill the empty can with milk and pour in, twice. Add eggs. Blend until smooth, about 30 seconds. Pour over caramel in the mold.
Place mold in a larger baking pan. Fill baking pan with hot water to a depth of 1 inch to make a water bath.
Bake pudding in the preheated oven until set and firm to the touch, 60 to 90 minutes. Remove mold from the water bath and let cool to room temperature, about 1 hour. Unmold pudding carefully onto a plate and chill before serving, about 3 hours.