The world faces escalating crises: record-breaking temperatures, widespread fires, severe flooding, increased oceanic microplastics, and unequal resource distribution. Academia introduces courses around sustainability to meet the new demand, but software engineering education lags behind. While software systems contribute to environmental issues through high energy consumption, they also hold the potential for solutions, such as more efficient and equitable resource management. Yet, sustainability remains a low priority for many businesses, including those in the digital sector. Business as usual is no longer viable. A transformational change in software engineering education is urgently needed. We must move beyond traditional curriculum models and fully integrate sustainability into every aspect of software development. By embedding sustainability as a core competency, we can equip future engineers not only to minimise harm but also to innovate solutions that drive positive, sustainable change. Only with such a shift can software engineering education meet the demands of a world in crisis and prepare students to lead the next generation of sustainable technology. This article discusses a set of challenges and proposes a customisable education roadmap for integrating sustainability into the software engineering curricula. These challenges reflect our perspective on key considerations, stemming from regular, intensive discussions in regular workshops among the authors and the community, as well as our extensive research and teaching experience in the field.