The integration of generative artificial intelligence (GenAI) technology in the realm of art and design has demonstrated significant positive effects on designers and related industries. The current study aimed to explore and evaluate the factors and personal traits that drive Generation Z to embrace GenAI-assisted design. The study model incorporated factors derived from the Unified Theory of Acceptance and Use of Technology 2 (UTAUT2), the Technology Readiness Index, and the concept of trait curiosity. Empirical validation was conducted using data collected from 326 participants in the southeast of Chinese Mainland. The results of structural equation modeling indicated that: (1) Factors such as effort expectancy, price value, and hedonic motivation from UTAUT2 have a positive influence on the intention to use GenAI, while performance expectancy does not show a statistically significant effect. (2) Both optimism and creativity significantly contribute to performance expectancy, effort expectancy, price value, and hedonic motivation. (3) Trait curiosity has a significant positive impact on both optimism and the intention to use GenAI. The research findings suggest the need for further improvements in the construction and operational strategies of GenAI platforms and provide practical insights for enhancing Generation Z's intention to utilize such platforms.