I've worked in nonprofit orgs, so I have a view towards this.
Good for you for figuring out how to prepare to do this work. It's important work, and not enough people are doing it.
There are two parts of any successful org. One is development (fundraising, grant-application writing, and contracting to provide services for governments and other orgs). It's business with a heart. For that work you'll need accounting and marketing skills and the gift of gab to deal with donors and grantors. You'll need some human-resources skills as well. If the org you serve contracts with governments, you'll also need to do collections: to get them to pay on time.
The other part of an org is generically referred to as "program." In your chosen field, the people you serve are vulnerable and in serious crisis. They're both survivors and victims of violent crimes. The people who serve them will need plenty of skill and also diligent peer supervision. In other words, it's demanding work and the people doing it need to take care of each other as well as their clients. They need the gifts of listening, caring, and advocating. And they need to be able to use those gifts for clients without burning themselves out.
Many of these people are licensed social workers and psychologists, with a physician or psychiatrist helping out. There may also be somebody with a background in law enforcement like a retired police officer, or maybe a lawyer. Those licensed people serve clients, and also serve as mentors to people working toward licensure.
If you're joining a small org, you'll probably need both kinds of skills.
The work you mention in your question is generically called "outreach." It's partly "program" and partly "development." It takes a fairly large org to have people whose primary job is outreach, so you'll probably need to do some other things as well.
If you want to concentrate on development, take business, marketing, psychology, and sociology classes.
If you're interested in program work. It might be wise to look for college classes in psychology and social work. You are on a career track that will eventually require a Master of Social Work degree, or maybe a psychology doctorate.
I strongly recommend you get in touch with an org that does this work in your area. Where I live, it's called the Jeanne Geiger Crisis Center. But your area has such an org too. Ask for a half-hour with somebody in charge, like the executive director, to get advice. Don't hesitate to ask for this: almost everybody in this field is delighted to give people like you a little time to help you along. And, you may be able to get an internship or volunteer position at the org . That will help you understand the nuances of getting the right training.
Again, good for you, and all the best.