Numerous studies have explored the impact of self-efficacy and a sense of belonging on STEM career selection and persistence, fostering identity development. Institutional support is pivotal for STEM students' academic progression and persistence. Such support includes educational guidance, mentorship, and cultural and athletic engagement. Evidence shows that these services enhance students' sense of belonging and motivation and influence their self-efficacy. This is particularly vital for first-generation college students. With its substantial first-generation and economically disadvantaged student population in engineering education, it is crucial to respond to this situation regarding self-efficacy, sense of belonging, and students' perceptions of access to institutional support. This research article explores the connection between students' sense of belonging, self-efficacy, and perceived institutional support in a private institution in Chile. We are particularly focused on unraveling how the university's services intersect with these socio-cognitive aspects, and this interest is amplified by the fact that a significant portion of the student body comprises first-generation university attendees. Our study encompasses 321 students pursuing various engineering majors at this university, where 60% of the student population belongs to the first-generation category. We analyzed survey responses assessing sense of belonging, self-efficacy, and institutional support. The survey explores three dimensions: 1) general belonging, 2) belonging in educational interactions, and 3) self-efficacy, each with eight items. The survey covers various aspects of the institution's student services, including psychological support, academic planning, tutoring, health and well-being services, sports, and supplementary areas like leadership, diversity, gender, and participatory meetings. It totals 29 items. Respondents expressed their views using a 5-point Likert scale, from "strongly agree" to "strongly disagree." Our findings reveal that all surveyed students exhibit a strong sense of belonging (both in general and within educational interactions) and self-efficacy. Notably, psychological support displays a significant and positive correlation with a sense of belonging, encompassing both general and interactional aspects. Furthermore, the sports and supplementary areas service exhibits a moderate and favorable correlation with the general sense of belonging. Conversely, the remaining services display relatively weak yet positive correlations with a sense of belonging (both in general and within educational interactions). Self-efficacy, on the other hand, maintains positive correlations with academic services, albeit of a weak or negligible nature, indicating a lack of a significant relationship between student services and student self-efficacy. These findings provide valuable insights into potential avenues for crafting institutional initiatives. These initiatives aim to foster students' sense of belonging and connection with the institution and bolster a significant psychological element crucial for academic persistence and advancement: self-efficacy. This is especially relevant in a school of engineering with a substantial population of first-generation students.