I recommend getting into a small company (i.e. 80-200 employees and profitable), if possible. At this size, you have opportunities to wear different hats and moving sideways, but you also get opportunities to see and participate in workforce scaling (helping form new processes, seeing new departments emerge, etc).

The important thing is to be vocal about what you want to do. If you came in as a frontend dev want to do more about backend work, go find gossip about new projects and express your areas of interest to higher ups. If you want manage people, offer to improve the technical hiring test. If something is stupid (maybe there's burnout due to too much overtime, or a process is over-bureaucratic, or some aspect of development is too cowboy), be proactive and offer solutions.

The unique thing about small companies is that there are enough people that narrowmindedness and complacency start to appear (and with it, process problems), which gives you plenty of opportunities to prove yourself with out-of-the-box thinking, but not enough bureaucracy to prevent you from being able to make changes.