Background/Objectives: Oral cavity cancer, a subtype of head and neck cancer, is one of the most common malignancies globally. This study assessed the influence of health system affiliation and pain manifestation on the risk of advanced oral cavity squamous cell carcinoma (OCSCC) in a Latin American population. Methods: In this retrospective cohort study, we analyzed medical records from 2015 to 2016, including data from the past 19 years, of 233 patients with OCSCC treated at a public hospital in Medellín, Colombia. Sociodemographic and clinical variables were evaluated, and multivariate regression models incorporated variables significant in bivariate analysis. Results: Among 233 patients, 196 (84.1%) had advanced OCSCC. The sample had a mean age of 63 ± 13 years, 53.6% were male, and 64% came from urban areas with predominantly low socioeconomic levels. Men showed a threefold increased risk of advanced OCSCC (95% CI: 1.3–6.8), while patients referred to pain clinics exhibited a 19.5 times higher risk (95% CI: 2.3–159.5). Patients in the subsidized health system or without health insurance had 2.6 (95% CI: 1.07–6.3) and 2.7 times (95% CI: 1.17–6.4) higher risks, respectively. Conclusions: This study found that male patients, referrals to pain clinics, and subsidized or no health system affiliation significantly increased the risk of advanced OCSCC.