Hmm. I think you mean 'go from feeling like a teen/kid into feeling like a normal adult'? When I was in my first job out of uni, I was the youngest on my team, and definitely felt it. I slowly progressed over a few years into being one of the ones to do the documentation and training, and felt pretty ok.
When that healthcare company was taken over by a for-profit shitshow and I had to jump ship, I applied for a lot of junior roles at various places. I got several calls, but the company that hired me was the one that offered me the senior position/lead instead. That made me realize "Oh, I guess I do know what I'm doing".
When I was heading up that group, I got a lot of management offers and when I finally departed to do consulting, it was because I had an appreciation for my professional worth. I did eventually leave that field because I just can't handle doing defense shit anymore, and that's really where the money is, but I still do ok.
My personal sense of 'not feeling like a kid' was probably when I started volunteering in my community, and doing a lot more to help the folks who needed it. When you develop strong friendships in the community that persist through things like illness and major life events, you have progressed beyond the whole 'drinking buddy' stage of friends.