Can an in-memory filesystem be created from inside a docker container with no special permissions?
Kubernetes can mount a ram disk for you. The answer is right there in the standard RTFM guide. 

https://kubernetes.io/docs/concepts/storage/volumes/#emptydir

Create an emptyDir volume and set emptyDir.medium to "Memory" to build, what I interpret from the documentation to be, a dynamically sized memory file system which counts against the containers memory limit.

If you're not running under kubernetes, whatever system that deploys the docker container would need to create the ram disk and mount that into the container, or give the container the special permissions discussed in the various reference articles in the question.