Generative products are significantly influenced by users and their unique ways of utilizing and adapting a product or cloud service to meet their needs. Centralized managed cloud services, such as SaaS solutions, often restrict and predetermine usage patterns, which is contrary to the principles of generative products. However, it is feasible to design generative products within the cloud context. This can be achieved by leveraging existing design patterns and rules, such as APIs, that facilitate generative cloud products. To fully harness the potential of generative products, product management must consider aspects such as patient play, meta problem-solving, hypothesis development, and user tinkering. These considerations impact the release life cycle of cloud products and are illustrated through examples of successful generative products.