Could it be possible in Craft Commerce to let an admin create a customer with a one time set billing address and that the customer can only set shipping address in the order process?
Currently there's not much in the way of back end support for creating customers as such. You can create craft Users in the back end, but given a commerce customer is not necessarily a Craft user, I think the short answer is no.
You could certainly create front end stuff that effectively achieves this though - how you prep all the form work for addresses is up to you, so you could e.g. force your checkout flow to go through a 'set billing address' page the first time and then simply never offers the opportunity to change that later.
You could even create forms for this part of the process that are only accessible by admin, so that you're creating your own 'back end' interface for this....and then pass off the created customers to your actual customers who then see a checkout that only lets them set the billing address.