M.J.
Maybe the teacher can help by pairing her up with just one student (someone known for being particularly nice) in class for a special project? It might be worth asking. That way she can build her confidence in the classroom environment and in a one-on-one situation. It may be that she's feeling really out of place with a large group but that if she gets to know someone one-on-one before recess, she'll be more comfortable when she gets the invite to join a group because she'll have that familiar person with her.
This is a huge transition time she's going through, so I can understand the nerves.
ETA: This just brought back a memory. We moved when I was in first grade and my teacher assigned me a "buddy" to show me around. Well, that buddy became my best friend and now 30-something years later, we're still friends.