Being an excellent customer service representative doesn't automatically make someone an excellent manager — management requires a different set of capabilities: leading and motivating employees, delegating responsibilities, giving constructive feedback, coaching, managing difficult conversations, resolving conflicts, setting expectations, monitoring performance, and communicating with senior management.
Look for opportunities to mentor new employees, help colleagues solve customer problems, lead small projects, train new team members, coordinate shifts, monitor team performance, or support process improvements. These experiences can demonstrate your readiness for management even before you formally receive a management title.