When your words, actions, and decisions may not be seen as 'leadership'.
I was responsible for my work, delivered on results, had no complaints from my stakeholders, was academically qualified, and was involved in project teams and various taskforces. Was that enough to be seen as a leader?
Apparently not.
A few key points for you:
Most organisations don't know what they are looking for in a First Time Leader.
Your best reference for leadership will be your direct manager.
Have a conversation on the leadership traits you need to display as a First Time Leader, and seek development opportunity for them.
If you are already leading others...
If your team members do not display much leadership, it might be because they don't know what they have to do. It starts with you specifying what traits you want to see in order for any of them to be seen as a leader.