Research with adults suggests that executive function (EF) might play a role in the development of divergent thinking, a key component of creativity, by helping children override canonical knowledge. We examined this possibility in two experiments, by manipulating the familiarity of objects used in the Alternate Uses test of divergent thinking both between-participants (Experiment 1: N=53 4-year-olds and 50 6-year-olds) and within-participants (Experiment 2: N=74 5-year-olds). We found evidence that younger children generated more and/or more original ideas for novel than familiar objects. However, this effect disappeared with age and did not depend on child EF. Further, EF was inversely associated with divergent thinking, controlling for age, intelligence, and income. These results call into question a simple executive account of children's divergent thinking and suggest that, among predominantly White, socioeconomically advantaged 4-6-year-olds, divergent idea-generation might be a primarily bottom-up process that can be hindered by top-down thinking.