Software-as-a-Service solutions are increasingly being adopted for delivering software applications, as they are scalable, cost-effective, and facilitate rapid deployment while providing high availability and flexibility. However, ensuring expected performance while tackling carbon emission concerns poses a significant challenge for the sustainable design and operation of software distributed over the cloud. The proposed research outline investigates Software-as-a-Service carbon impact throughout the main software development stages. As a first step, insights on the modeling and simulation of carbon-related metrics were derived from the lifecycle of a software system. The resulting knowledge led to the development of a reasoning framework enabling carbon awareness during the design phase of cloud-based software architectures. Future steps aim to integrate data visualization capabilities into the reasoning framework to understand the importance of the designed application features in the evaluation process and favor enhanced decision support. Furthermore, an adaptation framework is envisioned to handle uncertainty during the software runtime and keep the balance between carbon impact and performance under control. Together, these steps form a cohesive path toward carbon-aware Software-as-a-Service solutions design and operation.