With the continuous advancement of technology, automated vehicle technology is progressively maturing. It is crucial to comprehend the factors influencing individuals’ intention to utilize automated vehicles. This study examined user willingness to adopt automated vehicles. By incorporating age and educational background as random parameters, an ordered Probit model with random parameters was constructed to analyze the influential factors affecting respondents’ adoption of automated vehicles. We devised and conducted an online questionnaire survey, yielding 2105 valid questionnaires. The findings reveal significant positive correlations between positive social trust, perceived ease of use, perceived usefulness, low levels of perceived risk, and the acceptance of automated vehicles. Additionally, our study identifies extraversion and openness as strong mediators in shaping individuals’ intentions to use automated vehicles. Furthermore, prior experience with assisted driving negatively impacts people’s inclination toward embracing automated vehicles. Our research also provides insights for promoting the adoption of automated vehicles: favorable media coverage and a reasonable division of responsibilities can enhance individuals’ intentions to adopt this technology.