On the news portion of google, the only reference I could find to "Pebble-Cool" Rayon Acetate was this:
The Wellsboro Agitator (Newspaper) - June 15, 1938, Wellsboro,...
Subscription - Wellsboro Agitator - NewspaperArchive - Jun 15, 1938
... WHITE OXFORDS BOYS' WHITE OXFORDS w Mr HOLLYWOOD DRESSES of PEBBLE-COOL ACETATE AND SPUN RAYON Of cparse they're styled in Holly lovely style details. ...
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Lima News, The (Newspaper) - July 22, 1938, Lima, Ohio
Subscription - Lima News - NewspaperArchive - Jul 22, 1938
Most of these are jnade of Pebble-Cool cloth (acetate and rayon) and many are thc famous "Spun-rayons" Glorious Colors and Patterns. ...
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The Zanesville Signal (Newspaper) - June 2, 1938, Zanesville, Ohio
Subscription - Zanesville Signal - NewspaperArchive - Jun 2, 1938
HOLLYWOOD DRESSES I of PEBBLE-COOL ACETATE AND SPUN RAYON Of course they're styled in lovely style 5j details. They're made in cool pastel colors in rich ...
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And then, the only reference I could find to Loretta Young Fashion Frocks is this:
The Sheboygan Press (Newspaper) - June 9, 1938, Sheboygan, Wisconsin
Subscription - Sheboygan Press - NewspaperArchive - Jun 9, 1938
Loretta Young frocks may not swing you Into the but they'll give you the glamour of Hollywood with their neat patterns their youthful linea that make lovely ... Related web pages
Kid Sister
Time Magazine - Time - Mar 6, 1939
In a section of "Dos" and "Don'ts" middle-income readers are advised to go in for "romantic" cotton frocks like Loretta Young's, but to stop thinking about ... Related web pages
So with the deco-ish kind of font on the hang tag, the newspaper articles and ads being around the same time range, I'd say the latest it could be is mid 40's, and more than likely is early 40's or late 30's as referenced by the articles/ads.