Use your current job, if you’re actively hunting already! I don’t mean try to be a manager there - I mean, get their feedback on why they haven’t already made you a manager in your next 1:1.
Your boss may not know you want it, or they know you want it and can provide insight on what you have to do to get there.
I'll second/third this. When I was interested in becoming a manager, I talked to my manager about it and developed a long term plan to make the transition. This included stuff like going through internal company courses on management and incrementally taking on management-type responsibilities and tasks. I ended up changing my mind, but I'd say your manager can be a good resource for making that transition.
Your boss may not know you want it, or they know you want it and can provide insight on what you have to do to get there.