Mix milk, cream cheese, and salt in a mixing bowl; whisk together until smooth and foamy. Add sugar and arepas flour to milk mixture; mix with a spatula until dough is soft, thick, and workable, about 1 minute.
Divide dough into 4 portions (for the 4 wells in the maker). Form each quarter into a ball and use wet hands to gently shape it into a thick patty about 1/2-inch thick. If you see little cracks on the outside, the dough may be a little too dry; add more milk.
Heat arepas maker; lightly coat wells of the arepas machine with vegetable oil.
Place patties into wells of maker, close lid, and let cook through one cooking cycle of machine, about 5 minutes. For a crisper crust, flip arepas, using a wooden spoon or spatula, and repeat cooking cycle for 5 more minutes. Patties will be crusty and browned on both sides and the insides will be cooked all the way through.