How do I approach a girl I regularly see when I’m too introverted to start conversations?

I’m a university student and play beach volleyball once a week with the same group. There’s one girl there I’m interested in, and I’d like to get to know her better and see if there could be something more.

I’m quite introverted, so starting conversations is difficult for me. During the game I’m comfortable and we talk a little, but our interactions basically end when the game does.

I don’t want to suddenly make things awkward since we’ll keep seeing each other every week.

What's the best way to approach this? Should I first try to build more of a connection through casual conversations over a few sessions, or would it be better to simply ask her to grab a coffee sometime?

I’d especially appreciate advice from people who’ve been in a similar situation.