Climate change represents the defining global health challenge of the 21st century, with far-reaching implications for population health, health systems, and health equity. The acceleration of environmental change, evidenced by record-breaking global temperatures, extreme weather events, and ecological degradation, poses a direct threat to achieving Sustainable Development Goal 3 (SDG 3), which aims to ensure healthy lives and promote well-being for all. This manuscript examines the intersection of climate change and global public health in light of the outcomes of the 2025 United Nations Climate Change Conference (COP30) in Belém, Brazil. Drawing on recent global reports and emerging evidence, we explore how climate change exacerbates communicable and non-communicable diseases, undermines health system resilience, and disproportionately affects vulnerable populations worldwide. Particular attention is given to heat-related morbidity, infectious disease expansion, air pollution, food and water insecurity, displacement, gender inequities, antimicrobial resistance, and mental health impacts. The paper highlights the significance of the Belém Health Action Plan (BHAP), which places health more centrally within climate policy. However, major challenges remain, including voluntary implementation, financing gaps, and insufficient accountability mechanisms. We argue that achieving SDG 3 is no longer feasible without integrating climate adaptation and mitigation into health systems and policies.