I'm in a similar position at the moment. Basically what you want to do is ask for more responsibility from your PM, specifically to do work they'd normally do. Over time, that work will become part of your responsibilities. As you gain more confidence from doing those tasks, and as your team begins to recognize you moving away from programming and taking on more leadership, you'll put yourself in a good position to manage a sub-team on a small project. If you can pull that off, you can build on that for a bigger project/promotion to PM/SDM.

For example, we work in an Agile environment, so I've started running some of the 'Agile ceremonies', such as story refinement, estimation etc. From there my plan is to try and fully manage a sub team for a smaller project, as mentioned above. On top of this, I've arranged to go on a Project Management course in a few months. Doing all this should put me in a good position for a PM/SDM role.

Hope this helps and good luck!