This study examines the relationship between cultural capital and students' higher education (HE) expectations among six major origins of international students in U.S. HE institutions, using PISA 2018 data--the only cycle that measured global competence and related indicators of cultural capital. Through logistic regression analysis, it explores how non-financial assets like global awareness, interest in other cultures, and attitudes toward immigrants are associated with HE aspirations. The analysis reveals that cultural capital, such as home possessions and students' global awareness and interest in other cultures, positively correlates with students' HE expectations across these six origins. Conversely, parents' education levels and expectations for their child to complete HE show negative associations, suggesting a potential disconnect in the intergenerational transmission of cultural capital for international HE. This study highlights the complex dynamics between intergenerational cultural capital and global norms favoring the U.S. HE, offering insights into the inherently uneven global playing field.