My dd is 16. She has tons of friends and a busy social life, on top of everything else that she does. Tbh, as someone who was always quite shy and struggled with social anxiety, I am in awe of her networking skills!
Her friends come mainly from school, dance, drama, work and volunteering, and then she has met some others through her existing friends. Also, she says yes to opportunities through school and through her friends to do things that often bring her into contact with people who she hasn't met before...like next week she has signed up for a school project that involves none of her existing friends but will bring her into contact with kids of her age from a range of local schools.
One thing that I've noticed is that she is very good at making an effort to talk to different people when others might not bother. For example, she is the one who consistently makes an effort to go and talk to other kids in her classes, even when some of her closest friends are already there with her. She also makes a real effort to get to know the kids in the year above and year below her in school, through drama productions etc. She doesn't just stick to the comfort zone of people she already knows, and a few of her existing friends have commented on how her outgoing nature has helped them to expand their own social circles too, as she makes new friends who then get to know her old ones.
I think the other thing is that she makes a real effort to keep in touch with people she meets. Just loosely through social media etc, but she will make a conscious effort to check in with people and see how they're doing. I think it helps that she is really, genuinely interested in them and likes most people regardless of being able to see some of their flaws. A few of her friends can be a bit more judgemental and quick to find fault, and that perhaps limits their friendship options more. The way dd sees it, she isn't perfect herself and none of her friends are either, so if someone has a slightly annoying trait, she will try to look past it.
I hope that your dd can find some like minded friends soon!