There seems to be no end to what you can dig up on the Internet:

"LUCILLE BALL, one of the Goldwyn Girls appearing in Roman Scandals, arrives in New York today."
http://archive.org/stream/filmdaily64wids#page/n225/mode/2up

And ten days later, on November 13, 1933 was this: "LUCILLE BALL, Goldwyn Girl, left New York yesterday for Hollywood to appear in Barbary Coast for United Artists release."
http://archive.org/stream/filmdaily64wids#page/n287/mode/2up

And by August 1934, she was not only seeing her name in print, but also her face:

And by October 1936, she got a three-page magazine spread devoted to her:
http://archive.org/stream/movieclassic11moti#page/n135/mode/2up

October 1939, color:
http://archive.org/stream/photopla15chic#page/n373/mode/2up

October 1939, color:
http://archive.org/stream/photopla15chic#page/n373/mode/2up
Lucy was a hottie in the movies before she made her show.