There are likely a lot of entry-level positions. and you should focus on just getting your foot in the door, get the entry level and perform in such a way that you get noticed.
Make sure that as part of your interviews you ask about career progression possibilities - have others in this role progressed into other roles, etc.
Health insurance companies are generally pretty big, and that can provide a lot of different opportunities.
Also, no matter where you end up, network! get to know your boss, and your bosses boss. get to know managers in other departments and make your growth interests known.
The health care administration degree option wasn't really an option at the time most of us in the industry got into the field. Many a senior leader in the industry have gotten as far as they have with only a bachelor's and in a field of study that isn't quite as relevant as the health admin degree (e.g. business, sciences, history). It is their experience in the industry and performance in the roles within the company that get them far, but this degree field could help to get a foot in the door and lessens the learning curve a bit. There are, of course, leaders with MBAs or other degrees beyond a bachelors, but it is not the majority in my experience.
Kelly recommends the following next steps:
Karen recommends the following next steps: