Very nice goal! In many companies, there are entry-level project management roles (Junior PM, Junior Business Analyst, etc). That said, the project managers I work with mostly came into the role after being either in an account management role (more customer service/sales focused, which helps build communication skills) or from a line/production type role (software developer, implementation consultant, etc). As a PM, the more you understand the people working on the project team and what their tasks are, the better!
Definitely start looking into business and management courses that support building the competencies you need to be an excellent project manager. And there's lots of volunteer opportunities out there that will give you incredibly useful experience- working with nonprofits, there are tons of opportunities to work with mentors, take on and manage projects that will allow you to get experience and learn new skills.