No earlier than 1942, as this is when the older style veil was replaced by the trimmer coif illustrated here.(1)
The description reads:
American Red Cross Volunteer Special Service Corps, Washable Uniforms for Administration, Staff Assistant, Production, Braille, Canteen, Home Service, Hospital and Recreation and Paid Staff Workers (Except Hospital Workers).The uniform on the right would appear to be that of a Gray Lady (part of the Hospital and Recreation service.)
Even though commercially produced uniforms seem to have been readily available, the Simplicity company must have thought there was enough of a demand for a pattern to make this one available, as well as number 4694, home nursing pinafore and canteen apron.
Here's an example of a commercially produced uniform in the collection of the University of North Carolina.
No fabric recommendations are given, presumably because the ARC would have issued their own specific instructions on this.
(1) Shirley Powers's web site, http://www.collectarc.com/ was very helpful here.