I used to teach in child care centers, I have 3 of my own children and I have a home child care now.
I saw lots and lots of biting in the centers. I think the children were just very stressed out.
In that setting we tried to keep the children busy in centers and always watching and listening for conflicts. Sensory activities help out with this, too. Playdough, stress balls, bean bags (nothing that can be bitten open and toxic.) I made bean bags with "oil cloth" which is like vinyl, and rice, so I could disinfect them. The two year olds would bite them and their bodies would shake with the force. I didn't tell them to bite them, my plan was to play a toss game, but obviously it is a natural behavior.
In my child care home I have only had a biting incident 2 or 3 times in 10 years and never my own children. One time it was one girl who bit the same boy over and over. Her mom and I agreed that she would be by herself when it was free play time. She sat at the counter with coloring, puzzles, etc. When we had group games and circle time, and I was teaching, she joined us. This wasn't really a punishment or a time out, but it was our way of keeping the other child safe. It worked.
It would be very uncomfortable telling the child care provider what to do, but you could have your child bring a stuffed animal to squeeze. Also, if you have some ideas for the provider, you can pose them in questions. "Can my child sit by himself during play time?" " Can my child be kept away from the slide?" "What can I do at home?"
Good luck. I imagine you must be nervous. It will get better, just stay calm.