Preheat oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Combine flour, baking soda, baking powder, and salt together in a large bowl.
Beat sugar, butter, and queso fresco together in a large bowl. Add egg; mix well until combined. Mix in vanilla extract. Slowly mix in flour mixture, 1 cup at a time, until dough is thoroughly combined.
Shape tablespoonfuls of dough into balls and place 1-inch apart on baking sheets.
Bake in the preheated oven until set, 9 to 11 minutes. Cool on the baking sheets for 2 minutes. Transfer to wire racks to cool completely.