Heat the vegetable oil in a large skillet over medium-high heat. Add the onion and cook until softened, about 5 minutes. Add the garlic and cook, stirring, 1 minute. Add the beef and 1/2 teaspoon salt and cook, breaking up the meat, until browned, about 3 minutes. Add the tomato paste and chili powder and cook, stirring, about 2 more minutes.
Meanwhile, heat the refried beans in a small saucepan. Thin the sour cream with about 2 tablespoons water in a small bowl.
Spread the beans on the tostadas, then top with the beef and cheese. Drizzle with the sour cream. Top with lettuce, hot sauce and/or cilantro.