Mental health is a pressing concern in today's digital age, particularly among youth who are deeply intertwined with technology. Despite the influx of technology solutions addressing mental health issues, youth often remain sidelined during the design process. While co-design methods have been employed to improve participation by youth, many such initiatives are limited to design activities and lack training for youth to research and develop solutions for themselves. In this case study, we detail our 8-week remote, collaborative research initiative called Youth WellTech, designed to facilitate remote co-design sprints aimed at equipping youth with the tools and knowledge to envision and design tech futures for their own communities. We pilot this initiative with 12 student technology evangelists across 8 countries globally to foster the sharing of mental health challenges and diverse perspectives. We highlight insights from our experiences running this global program remotely, its structure, and recommendations for co-research.