Don't try to get her to come out of her shell.
Let her observe and move at her own pace.
If she's like most of us, she needs time to see who she is playing with, how they treat each other, and how the GM manages conflict.
Once you've created a safe environment, she'll come out as far as she is comfortable. It may take a few weeks or a few months, but she'll take the risks when she's ready to take the risks.
If you force her out before she's ready, she's likely to clam up entirely or even not return.
Some people are going to be very quiet -- don't worry about that, just do your best to make sure she has fun. Give her character some opportunities to shine (which hopefully you're already doing for all the PCs), and then maybe solicit some feedback from the group after each session about what their favorite parts were, so you get a better idea about what parts of the game she enjoys (while also learning what the rest of your players were enjoying most, too.)
Is it really a problem ?
Either way, don't force it. Some people take more time than others getting comfortable in a new context. That's fine.
Giving her opportunities is probably good, as is not insisting heavily or putting everything on her to force her to act.
If, medium to long term, it doesn't seem to change or it becomes an issue, maybe talk to her.
But I wouldn't worry about it, time will likely be enough.
I play with my wife and she was this way. Let me ask you something, did you make her character? Or does she know what her character can do? I made this mistake. And too be honest my wife said just make her a character. I corrected this after a few games but there is difference when they make their own characters.
Her brother helped her make it
That’s what I thought. How I helped get my wife to be more comfortable is I made her recreate her character. She thought it would be weird but I told her I have had so many characters in her past it really doesn’t matter. Instead of being an operative she became a technomancer and likes it a lot better.
But if your daughter really likes her character and doesn’t want to change make her make the same character from scratch. Then make sure she understands her skills and what each one does. Since the skills do multiple different things she might not know what she can do. Maybe write the skills down on flash cards and write what the skills can do on them with DC checks. We did this with her spells and skills.
Then again like everyone else said it just might take time.