There are many reasons she isn't doing this. It could be she just hasn't seen any other kids playing. I had a couple of kids, over the span of about 13 years in child care, that came to my center when their mom had to go back to work.
One lost her husband and had no source of income to support her daughter. The other one was a guy who had custody of his toddler son and he just didn't know what to do. The mom had been totally wasted during her whole pregnancy. She was still unable to even visit the child because she was so strung out.
Both of these kids had issues that were similar to what you're describing.
The boy would stand and stare off into space, until another kid tried playing with a toy that somehow that boy had decided was his I guess. He never did get to a point where he would engage and play successfully. He had to leave our facility due to aggression to other kids
The little girl took a long time. She would be on the fringes of the groups, they would invite her frequently at first. She would watch the kids in the pretend play area dressing up and playing in the household area. Then she'd wander over and watch kids read books in the bean bag area then I'd see her over watching the kids building with blocks, puzzles, painting, or some other activity.
She took about 5-6 months before I saw her actually join a group. She did fine after a while, it just took her a long time. I am not sure she'd ever seen other kids before. The mom was a very nice person but I'm not sure she knew how to teach her child to play or interact with other kids. I don't know if she'd even played with any before coming to the center.
I'd see about finding a Mother's Day Out Program. These programs are usually very informal. They do follow a daily schedule, that's not what I mean. They don't do a steady enrollment where you "have" to be there every day or lose your spot like child care. You sign your child up for one day, two days, or three.
They are often at a local Methodist church in my state. We have 2 different churches in our area. One is open 10am-3pm Monday, Wednesday, and Friday's. The other place is open 9am-noon on Tuesday's and Thursday's.
Now, on the other hand. Your child could have an issue that needs to be diagnosed. I'd think having her seen by someone that does professional evaluations for developmental delays or things like Autism. If for nothing else than knowing what it's not.
If she is diagnosed with a delay or gets a diagnosis then she might be able to start school in an early education program. Kids who have any sort of handicap are legally eligible to start public school at age 3 so they can get a good start on learning the things they need to.
I have a friend who's son had only a hearing problem. His test results showed he was partially deaf. He started school the day he turned 3. His mom wanted him to have the best chance to learn in the best possible way.
I hope you find the resources you need for your little one. GOOD LUCK!!