As a female who became a police officer with a degree in Sociology, let me offer some advice. . .
First things first, to get to detective, you have to be a police officer first! Have to crawl before you can walk. So, concentrate on doing the things you need to do to become an officer. This means being physically fit, having good upper body strength, flexibility, endurance, etc. Having a background in teamwork helps, such as sports. Keep your reputation untarnished. Avoid drugs, bad people, etc. Don't cut classes. Be respectful to all, as the background check may involve talking to teachers, neighbors, ex-boyfriends. etc. Pay your bills. Law enforcement agencies normally do not have enough women, so, yes, it is easier for us to get hired. But, you need to be able to pull your weight and prove yourself to your fellow officers. Every rookie does - male and female.
Now, about Detective. Police officers are constantly taking more training. It is a requirement, so you stay current. Beyond that, I would encourage you to try to become a Field Training Officer, where you are responsible for training up new recruits once they graduate from the academy. It looks good on your record.
What major? Sociology/Psychology teach us a lot about people. Honestly, you will learn most of that from experience as an officer anyway. But, if it was me, and I had aspirations of being a detective, I'd look to add a minor in something like cyber security, forensic science, etc. Crimes are becoming more and more high tech. While you will get detective training if promoted to detective, you will learn more from it if you have at least been exposed to some science/technology.
Let me know if you have any questions.