This study evaluates the integration of the Sustainable Development Goals (SDGs), focusing on SDG 13 (Climate Action), in higher education and its impact on students' awareness and knowledge at the Universitat Politecnica de Valencia. Given the urgency of addressing climate change and its repercussions, the research highlights the pivotal role of education in fostering understanding and engagement with the SDGs, particularly among engineering students. The study utilized pre- and post-awareness session surveys to assess the prior knowledge and subsequent learning progression concerning SDGs among students from the School of Telecommunications Engineering and the School of Agricultural Engineering and Environment. Results indicate a significant knowledge gap, with over 60% of students unaware of the SDGs. However, following targeted educational interventions, a marked increase in SDG comprehension and interest was observed, particularly among students from the agricultural and environmental engineering school, reflecting disciplinary influence on sustainability receptivity. Gender differences emerged, with women more aware of climate change's present effects while men expressed greater interest in future-related issues. Older students demonstrated better content assimilation, and public education students showed higher SDG awareness than those from private institutions. The study underscores the necessity for personalized education strategies and a revised approach to integrating SDGs into curricula and research projects to enhance the effectiveness of sustainability education in preparing future professionals to contribute to global sustainability challenges.