I don't have source for this artifact.
However, the video below shows another textile and offers a source.
1920, Paper Doll Baby Bobby.
The march toward gender-specific clothes was neither linear nor rapid. Pink and blue arrived, along with other pastels, as colors for babies in the mid-19th century, yet the two colors were not promoted as gender signifiers until just before World War I—and even then, it took time for popular culture to sort things out.