Sympathy. Is there a huge self esteem issue beneath this eg negative self-talk, impostor syndrome, fear of humiliation and failure…or is she simply not a queen-bee/social butterfly type?
Is an adult awarding the opportunities (like picking the lead cheerleader) or is it a peer-group selection process (like choosing a team captain for debate club?)
or is it a case of volunteering for a spot or needing to be “grabby” to claim an activity from a particular person who is socially stronger?
is it competitive and is it mixed sez or just girls? That makes a difference too.
I remember a light bulb moment watching an episode of Oprah (which ages me!) in which she discussed lots of famous people who consider themselves lacking confidence - it was also the first time I heard about impostor syndrome. Oprah interviewed an expert discussing a “fake it til you make it” approach in which she described how acting confident helps: you speak louder, you maintain eye contact, you smile more etc. It works like the “fourth wall” in acting. People respond differently to you when they perceive you are confident, and that becomes a virtuous circle.
So i would avoid books - I’d go for TED talks and interviews with famous people.
You could also try going at it from a tangent - there are some brilliant films and series about people overcoming adversity, or understanding sports psychology (how people/ teams use failure to become learners/gold medalists). I absolutely love watching films about free climbers - a completely different mentality to my own.
Or watching some stuff about Adele (dreadful stage fright) and Lady Gaga (uses clothes as a way of shielding herself). Realising other people have succeed from a weak starting point can be enlightening.
Understanding what makes people tick, and how people can manage their own thoughts and feelings is helpful. As you can learn a lot from seeing how the best people have done it. And then recognising what is holding you back and making small steps comes next.
I would also sort of get her to imagine in her head the best way to manage a social situation. If she cannot yet imagine herself walking into the group last with a bright smile and a breezy “hey I’m here! Did you miss me?” Then her approach should be to arrive FIRST (or nearly first) so she is the one welcoming people. A “you made it! Yayyy I’m glad you are here as we are just talking about x and I wanted to ask you….” is socially easier than a splashy late arrival but still gives you a bit of a social lift compared to being middle-pack.