Background and Objectives: Sentinel surveillance in the early stage of the COVID-19 pandemic in Mexico represented a significant cost reduction and was useful in estimating the population infected with SARS-CoV-2. However, it also implied that many patients were not screened and therefore had no accurate diagnosis. In this study, we carried out a population-based SARS-CoV-2 screening in Mexico to evaluate the COVID-19-related symptoms and their weighting in predicting SARS-CoV-2 infection. We also discuss this data in the context of the operational definition of suspected cases of COVID-19 established by the Mexican Health Authority’s consensus. Materials and Methods: One thousand two hundred seventy-nine subjects were included. They were screened for SARS-CoV-2 using RT-PCR. The weighting of COVID-19 symptoms in predicting SARS-CoV-2 infection was evaluated statistically. Results: Three hundred and twenty-five patients were positive for SARS-CoV-2 and 954 were negative. Fever, asthenia, dysgeusia, and oxygen saturation predicted SARS-CoV-2 infection (odds ratios ranged from 1.74 to 4.98; p < 0.05). The percentage of asymptomatic COVID-19 patients was 36% and only 38.15% met the Mexican operational definition. Cq-values for the gene N of SARS-CoV-2 were significantly higher in asymptomatic subjects than in the groups of COVID-19 patients with neurological, respiratory, and/or musculoskeletal manifestations (p < 0.05). Conclusions: Dysgeusia, fever, and asthenia increased the odds of a positive result for COVID-19 1.74–4.98-fold among the study population. Patients with neurological, respiratory, and/or musculoskeletal manifestations had higher viral loads at COVID-19 diagnosis than those observed in asymptomatic patients. A high percentage of the participants in the study (61.85%) did not meet the operational definition for a suspected case of COVID-19 established by the Mexican Health Authority’s consensus, representing a high percentage of the population that could have remained without a COVID-19 diagnosis, so becoming a potential source of virus spread.