Generative Artificial Intelligence (GenAI) is being adopted for a number of Software Engineering activities, mostly centering around coding, such as code generation, code comprehension, code reviews, test generation, and bug fixing. Other phases in the Software Engineering process have been less explored. In this paper, we argue that more investigation is needed on the support that GenAI can provide to the design, and operation of software systems, i.e., a number of crucial activities, beyond coding, that are necessary to successfully deliver and maintain software services. These include reasoning about architectural choices and dealing with third-party platforms. We discuss crucial aspects of AI for software systems. taking as a use case Function as a Service (FaaS).We present several challenges, including cold start delays, stateless functions, debugging complexities, and vendor lock-in and explore the potential of GenAI tools to mitigate FaaS challenges. Finally, we outline future research into the application of GenAI tools for the development and deployment of software systems.