Given the growing need for sustainability in engineering, there has been an increased emphasis on introducing sustainability in the engineering design curriculum. Towards this end, several researchers and educators have proposed educational initiatives for integrating sustainable design in the engineering design curriculum, as early as in the first year of study. However, these initiatives are only as successful as students' ability to relate to the issues related to unsustainable behavior and take active measures towards these issues. Prior research has suggested the influence of empathy on designers' ability to relate to the users' needs. In the context of sustainable design, students must not only relate to the needs of the primary user but also empathize with those indirectly affected by their decisions. However, little research has explored the influence of students' trait empathy on the outcomes of sustainable design education and we aim to explore this research gap. Specifically, we introduced first-year engineering students to a two-day workshop on sustainable design approximately three-quarters of the way through their semester-long design project. At the end of the semester, students were asked to reflect on the utility of the workshop towards both, empathizing with the user, and designing sustainable solutions, in their semester-long projects. From our results, we see an increase in students' attitudes and intentions towards sustainability from before the workshop to the end of the semester. On the other hand, we see no differences in students' trait empathy. A qualitative analysis of students' reflections showed that students had a positive experience with the sustainability workshop and that they were more inclined to incorporate sustainable design practices into their project after participating in the workshop. These findings suggest the need for future work on the role of empathy development in encouraging a sustainable design mindset among engineering designers.