Odds of Getting In
There will never be a lack of need for obstetricians. As long as they're making babies, you'll have a patient roster that multiplies every day. There are a huge number of programs available for med students seeking OB/GYN program residencies, and nearly all of the available slots are going to college seniors in the U.S.
You don't need to take pre-med courses for medical school, and there are several ways to get closer to a career in obstetrics. You might do health care aide or tech work in a clinical setting, or as an ultrasound technician or a Certified Nurse-Midwife (CNM).