The students' perceptions and experiences about the organizational attributes of the higher education institution in which they are enrolled seem to have a strong influence on their integration, sense of belonging, and commitment to their new academic reality. The present paper focuses on the analysis of how first-year students build a sense of belonging and commitment to the higher education institution that welcomes them, focusing on institutional attributes that can act as (positive or negative) catalysts, such as physical and cultural dimensions. However, besides physical and cultural dimensions, it is crucial to consider its synergies with psychological, social, organisational, political, and axiological dimensions that have emerged as critical variables for contextualizing the analysis. The results suggest that the physical dimension nourishes the students' feelings of belonging, namely through the felt need to develop skills to manage their interaction with the spatial dimension of the institution that welcomes them. Moreover, newcomers' self-concept seems to be significantly increased by the feeling that they are now part of a cultural but also social elite. On the other hand, the feeling of integration seems to be supported basically on successful peer relationships. This perceived prestige of the higher education institution where they now belong represents, "a anteriori," a crucial demand for the career management of the Bourdieu' "heirs," and, "a posteriori," a real (and sometimes surprising) achievement for first-generation students.