G.B.
I would say that you need to re-think this if you truly have no friends. I have neighbors who we put on the forms, friends from church, friends from the community. If you don't pick up your child from child care on time they can call the police to have your child picked up for being abandoned.
You MUST put other people on that contact list. That is the emergency pickup person. You would call that person in the event that you are not going to be there to pick your child up.
It is your responsibility to notify the person on the list and then confirm to the child care provider that they can expect XXX to pick up your child.
Otherwise choose a child care setting by your work and pick kiddo up before getting on the public transportation.