The following outtakes of famed Cuban dancers Raúl and Eva Reyes dancing the rumba in 1935 have been made available by the Moving Research Image Collections at the University of South Carolina:
According to the Library, the video contains footage of “Dancers Raoul and Eva [Reyes] with [Paul Sabin and the] Siboney Sextet orchestra, performing a rumba to entertain guests on the Roney Plaza Hotel beach front.” The footage was filmed in February, 1934. It is listed by the Library as Fox Movietone News Story 21-173.
The rumba of the 1930s appears notably faster than modern rumba. Walter Nelson discusses the particulars of the 1930s rumba here. He has put together an interesting montage of rumba dancing from 1930s movies. It is viewable on youtube:
The cover photo for this post, which features Raúl and Eva Reyes in the same costumes they wear in the video, was discovered on ebay.