Generative AI, such as ChatGPT, Google Gemini, Bing CoPilot, and similar models, bring changes in how students interact and search for knowledge online. Researchers are increasingly interested in exploring the factors that influence this change in student interaction with generative AI. This study examines the factors that influence students' intention to use generative AI in the context of a Bangladeshi engineering university. As part of a larger study, this research reports initial findings from pilot data. Based on the Unified Theory of Acceptance and Use of Technology (UTAUT), the study examines the role of social influences and cognitive processes in AI adoption of students. Using a quantitative research approach, the study reveals that factors such as social influence, student image, job relevance and perceived usefulness significantly influence students' intention to use generative AI. While male and female students have similar attitudes towards the use of generative AI, local students significantly differ from international students in perceived usefulness, perceived ease of use, and result demonstrability of generative AI tools. These observations can guide educational institutions to integrate generative AI models in the learning environment and offer more interactive and personalised learning experiences for students.