If you want to advance your career, it's important to demonstrate leadership. How can you take up the mantle without being selected for a new role at work first?
The best opportunities are going to come from your personal interests. In your social and interest groups, there are plenty of events and groups to get involved in and help organize. For example, sports teams need some coordination and planning for events and travel. Book clubs have responsibilities to find a place to meet and let everyone know the details. You can seek out academic groups or start a tech meetup for more professional engagement.
These experiences will help build your understanding and insight as a leader. When applying for new roles, you can speak to what you learned about collaborating with other leaders to form a plan and facilitate group activity. You have to start somewhere, and having something you're passionate about will help you keep progressing.