So can you have a bigger set of Glutes naturally? Of course you can. You can even build them up from a small flatter butt to a plump bigger one. But genetics will predetermine how big your Glutes will and can get. But yes everyone can potentially have a bigger, more rounded Gluteus.
The way to achieve this is by hard work. Hard work done in the gym with various exercises to help target the Glutes. Some of these exercises are: Ass to Grass Barbell Squats, Pelvic Lifts(called Hip Thrusters), Lunges, Deadlifts, Glute Kickbacks, etc..In order to achieve this you need to do a hypertrophy(muscle building) protocol.
An example of this is a pyramid set at heavier weight of 4 sets of 8-12 reps. A pyramid set is just increasing the weight after each set. You will need to do this workout 2-4 times per week..
It should take at least 4-6 weeks to start seeing and feeling a harder butt and longer after that to see a definitive difference. As in your Glutes looking noticeably larger.