All kids and all people are different. I think it is okay to try to help your daughter through and guide her with things she can do to increase her friends and playtime. I certainly would. The real question is . . . is she bothered by this? Some people don't require tons of friends. If she can find just one really good friend, she will be on her way.
So, I'd try some different things. What does she like to do? Girlscouts are an excellent activity for someone a little shy. If she likes tumbling or soccer or dance---- you can sign her up for an activity like that. Then you become friendly with some of the other moms too and maybe something could blossum.
You could also talk to her teacher and see if there are any kids in her class that would be good friends canidates that she could pair you daughter up with for some projects . . . And also, at my kids school, the couselor there runs friends groups that get small groups of kids together for the purpose of helping with this process.
Good luck----- wishing her that one friend to make her feel special and many more to follow after that . . .
Thank you for the advice. She is in Girl Scouts and does Aikido, although that is mostly boys.
The school counselor also suggested doing a friends lunch, allowing my daughter to invite a few friends to lunch with the counselor.
I am hopeful that she will find some friends and create helpful bonds.
Thank you again, great advice!