I will edit this with a source later as I don't have the book with me but I recall that in Henry Miller's Air-Conditioned Nightmare, he does refer to dates like the 1870s as "the 70s", etc. So there is one primary source of someone doing that. Perhaps it started in the 19th century? Can someone expound on this?

The title of the Mae West film Belle of the Nineties refers to the 1890s. The Shirley Temple film The Little Colonel opens with a title card reading "Kentucky in the 70's", meaning the 1870s. Both movies were released in the 1930s.