The implementation of Agenda 2030 and the Sustainable Development Goals (SDGs) by the United Nations in 2015 focuses on making a more sustainable world in all countries and for all stakeholders. Higher education institutions (HEI) play a key role in increasing students’ sustainability knowledge, transforming their attitudes and motivating them to promote or engage in sustainability behaviors. HEI can take several measures to fulfill these objectives, but it is important to develop efficient tools to assess the starting point at which university students are at. In this study, a survey was conducted that addressed students from different Universitat Politècnica de València (UPV) degrees to investigate their knowledge and awareness of sustainability and SDGs. This survey (n = 321) showed students’ levels of knowledge and initial awareness. Many UPV students state that they are aware of the SDGs, but most do not fully understand these 17 goals and their current implementation but think that the SDGs are important for their daily lives. Therefore, finding links between the SDGs and daily interests is necessary to advance toward further implementation to allow us to fulfill all SDGs. These results offer a good starting point for evaluating future training and awareness actions to improve sustainability-related educational strategies.