The current prevailing trend in design across key sectors prioritizes eco-design, emphasizing considerations of environmental aspects in the design process. The present work aims to take a significant leap forward by proposing a design process where sustainability serves as the primary driving force. In this context, sustainability is positioned as a fundamental component to be integrated into the initial stages of design, introducing innovative multidisciplinary criteria that redefine the design paradigm. Within this framework, sustainability is characterized using a comprehensive and quantifiable index encompassing technological, environmental, economic, and circular economy dimensions. To demonstrate the practical application of sustainability as the primary criterion in designing mechanical components, a parametrized finite element model of a composite plate is utilized, integrating both pristine and recycled fibers. Subsequently, a demonstrator derived from the aviation industry—specifically, a hat stiffener—is employed as a validation platform for the proposed methodology, ensuring alignment with the demonstrator’s specific requirements. Various representative trade-off scenarios are implemented to guide engineers’ decision-making during the conceptual design phase. Additionally, the robustness of the aforementioned methodology is thoroughly assessed concerning changes in the priority assigned to each sustainability criterion and its sensitivity to variations in the initial data. The significance of the proposed design methodology lies in its effectiveness in addressing the complex challenges presented by conflicting sustainability objectives. Furthermore, its adaptability positions it for potential application across various sectors, offering a transformative approach to sustainable engineering practices.