No, Jack Nicholson's first film was not "Little Shop of Horrors". Nicholson's first film was "The Cry Baby Killer", which was released in 1958. He played the lead role of a teenager who gets into trouble with the law.
While it's true that Nicholson appeared in "The Little Shop of Horrors," it wasn't his first film. He had a small role in the 1960 film, which is a low-budget, dark comedy about a man-eating plant. Nicholson played a masochistic dental patient in the film. This film has become a cult classic and is often mistaken as his first film due to its popularity.