GenAI has a potential to enhance the learning and teaching processes in engineering education. For instance, GenAI feedback on students' task performance can be effective depending on when such feedback is provided. However, little is known about how engineering faculty and instructors discover such potential within the scope of their instruction when they try out the technology for the first time. To this end, this study purported to describe an engineering instructor's and seven teaching assistants' initial experiences of integrating GenAI into their undergraduate engineering course and the corresponding changes in students' formative exercise performance. An embedded descriptive single case study design was employed. The corresponding research data included four interviews conducted at the beginning, middle and end of an academic semester, and students' formative exercise performance. Overall, after GenAI integration, students' formative exercise performance increased, and a critical and reflective practice of learning about how to integrate GenAI into instruction provided informative insights. Still, technology integration stayed at the level of replacing other instructional methods or increasing the efficiency of solving coding problems. It turned out to be exciting and surprising for students to be able to use GenAI in course work even though their use of the technology weakened over time. Our findings suggest that engineering teaching staff's initial experimental experiences with GenAI integration can be informative and provide context-specific practical insights. Therefore, it is reasonable for higher education institutions to encourage such experiences especially when there is a lot of unknown regarding an emerging technology.