Divergent thinking is the ability to produce numerous and diverse responses to questions or tasks, and it is used as a predictor of creative achievement. It plays a significant role in the business organization's innovation process and the recognition of new business opportunities. Drawing upon the cumulative process model of creativity in entrepreneurship, we hypothesize that divergent thinking has a lasting effect on post-launch entrepreneurial outcomes related to innovation and growth, but that this relation might not always be linear. Additionally, we hypothesize that domain-specific experience has a moderating role in this relation. We test our hypotheses based on a representative longitudinal sample of 457 German business founders, which we observe up until 40 months after start-up. We find strong relative effects for innovation and growth outcomes. For survival we find conclusive evidence for non-linearities in the effects of divergent thinking. Additionally, we show that such effects are moderated by the type of domain-specific experience that entrepreneurs gathered pre-launch, as it shapes the individual's ideational abilities to fit into more sophisticated strategies regarding entrepreneurial creative achievement. Our findings have relevant policy implications in characterizing and identifying business start-ups with growth and innovation potential, allowing a more efficient allocation of public and private funds.