Do good work, be interested and show interest, and be in a recipiable environment.

If your current environment is overbearing with power politics you don't succeed in and you want change you'll probably have to change environments.

If you want impact consider whether smaller companies and teams would be beneficial. You may be able to fill your desires of impact and control even without becoming a formal lead role. Or become one implicitly or naturally quicker in smaller less formal and structured environments.

You can also look for job offerings for those kinds of roles specifically. No need to seek out a climb in house when you can find more direct routes.