There are so many actions and things you can do in any organization that can show you are a leader far before someone will even consider that you should bear the title.
Take action. Speak up. Think big. Challenge your peers for a better outcome. Help peers and teams get things done. Earn trust. The list goes on.
Just take a look at the 14 leadership principles from Amazon. Except maybe for the hiring part, you can progress and perform in any of the other categories without the need of a title or a team.