This paper presents the outcomes of a study of first-year engineering student perceptions of creative opportunities in engineering design tasks. The study was guided by three key questions: (1) How do first-year engineering students view creativity and its role in engineering? (2) What opportunities do students see for creativity in their engineering design projects? (3) How do various factors, including the course structure and the instructor, influence student choices to pursue creative opportunities? First-year engineering students participated in four surveys during the semester in which they were working on an engineering design project. Overall, the participants perceived many creative opportunities; however, the opportunities they saw at the beginning of their work were greater and broader, while once into their projects, the scope of their perceptions narrowed. Throughout the design project, the instructor, project constraints, and risks associated with exploring a creative design option influenced the participants' perceptions. The research outcomes can guide how instructors advise student decision-making and structure their design courses to facilitate creativity.