It’s normal if they are slow to warm up. So if she doesn’t talk now, she will eventually feel comfortable after building trust and will engage. But if you do notice that she doesn’t warm up at all and talk to anyone or leave your side except for certain/same people, it could be selective mutism- a form of anxiety with choosing to only speak to certain people (but she’s only 2 and language may be limited anyways) Or could maybe be something else. I would recommend seeking support if you’re not sure. It doesn’t hurt to rule anything out.
I had selective mutism as a child and my mom forced me to interact with others even when I was uncomfortable. She was frustrated and embarrassed because of me and always making excuses. Do not do this! I’m still in therapy trying to salvage my hurt and my relationship with my mother is strained as a result. I would advise that you respect her needs and allow her to be alone or quiet and make sure your own social needs are met. She might just want to observe. She also may lack the skills and confidence to communicate with others and need a bit more explanation or observation time.
My daughter is super shy too! She’s in gymnastics and we go to a toddler class 1x a week- still she’s just a shy girl. I’m sure she’ll grow out of it- my SILs son is the same age and he is the farthest thing from shy - but everyone is different she’ll open up -the world is a totally new thing for them, plus there’s a lot of brain development goin on 💗