The objective of this paper is to present the design of a precursor mission for the Planetary Sunshade System, positioned near the photo-gravitational equilibrium point L1*, located between the Sun and the Earth-Moon system's center of mass. This study pioneers the integrated system engineering design and mission scenario definition. Earth's climate change, driven predominantly by the escalation of greenhouse gases in the atmosphere, poses an unprecedented threat to global stability and sustainability, manifesting through increased global temperatures. In response, a space-based geoengineering infrastructure has been previously proposed as a mitigation measure. It would enable to reduce the oncoming solar irradiance, by placing a 'solar-light umbrella', called Planetary Sunshade, strategically positioned between the Sun and the Earth. The proposed Planetary Sunshade precursor mission aims at pushing forward through in-space testing some of the critical enabling technologies for such a space-based climate change mitigation solution. First, the precursor Planetary Sunshade System and mission requirements are discussed, for the first time to the best knowledge of the authors. Emphasis is put on the astrodynamics of the mission, analyzing the orbital regimes suitable for maximizing efficacy and stability. Then, the system design is introduced, based on small satellite components, focusing on critical aspects of subsystems such as solar sail, attitude and orbit control system, deployable structures and mechanisms, thermal system, and telemetry. Particular attention will be paid to the choice of solar sail materials, emphasizing their optical properties. This precursor mission is meant to serve not only as a proof of concept but also as a critical technology testbed. By studying the feasibility of such a mission, we contribute to a broader discussion on possible space-based interventions for climate change mitigation. Our work aligns with several UN Sustainable Development Goals, notably SDG 13 (Climate Action), by exploring innovative solutions to mitigate climate change, and SDG 9 (Industry, Innovation, and Infrastructure), by pushing the boundaries of current space technology.