The urgent commitment of educational institutions to achieve Education for Sustainable Development leads us to propose studies such as this one. In particular, the main objective of this study is to analyze the degree of awareness and knowledge about the Sustainable Development Goals (SDGs) among students studying Education Degrees (Degree and Master) (n = 153) at a public university, and their perception of the possibilities of working with them. The mixed methodology and ad hoc questionnaire validated by experts allowed for a descriptive and inferential analysis of the data. The results suggest that there is a need to improve awareness, training, and implementation of the SDGs in university teacher training. Some improvement was perceived when comparing prior and final knowledge, with a significant association detected between the latter and the academic year. Of all the educational stages, Higher Education is considered the most favourable for working on the SDGs, with university students becoming promoters of this challenge. In general, they consider that SDGs 4, 5, 3, and 16 (in that order) require the most attention, with significant differences depending on the academic year. The study calls for a review of the curricula for Education Degrees, and for the implementation of more teaching, research, and institutionalization initiatives to address the challenges of the 2030 Agenda.