The accelerating impacts of climate change, including rising global temperatures, extreme weather events, and increasing carbon emissions, are intensifying the demand for sustainable and climate-adaptive construction practices. Conventional construction materials such as cement, steel, and concrete, while critical for modern infrastructure, contribute significantly to greenhouse gas emissions and exacerbate the environmental footprint of the built environment. This paper explores the potential of green and low-carbon construction materials as foundational elements in designing climate-adaptive civil structures. Specifically, it examines the life-cycle environmental performance of alternative materials such as geopolymer concrete, recycled aggregates, cross-laminated timber (CLT), bamboo composites, and phase change material (PCM)-enhanced concretes. These materials not only reduce embodied carbon but also improve thermal efficiency, resilience, and adaptability under climate stressors. The paper integrates insights from life-cycle assessment (LCA), material innovation research, and adaptive design strategies to propose a holistic framework for sustainable construction. Furthermore, digital technologies such as Building Information Modeling (BIM) and material passports are discussed as enablers of circularity and low-carbon supply chains. By analyzing recent advances and case studies, this study demonstrates how climate-adaptive materials can reduce construction-related CO₂ emissions by up to 40%, extend service life under extreme conditions, and support global carbon neutrality targets. The findings underscore the urgency of mainstreaming low-carbon materials into infrastructure planning, highlighting their role in transitioning toward resilient, sustainable, and climate-conscious civil engineering practices.