I had a friend growing up who was like this. Kids were giving her grief on the playground in K because, they said, "she can't talk." I marched right up and asked her, kindly, "Can you talk?" She nodded. I turned to the kids teasing her and said, "There. She can talk. Now, leave her alone!"
I didn't hear her speak at school for years, but when I played with her at home, she was downright loud! I was surprised the first time I played with her at her house because of how different she was there. I think it was later elementary school before she said anything at all in school though.
She eventually grew out of the selective mutism--which we just called shyness at the time, though I really think it was the same thing you're dealing with. She and I were friends into college, and we still keep in touch sometimes even now. That's 30+ years!
I don't know if this will happen with your child, of course, but I hope it gives you hope.
