Accessibility measures the ease at which an individual can access a desired location. It is a major aspect in transportation planning, and transit systems are extensively used to improve accessibility. Well-designed public transit systems enable a high level of access to socioeconomic opportunities. This is especially important to socially disadvantaged populations due to their higher need for transit services to maintain a basic level of mobility. Increased transit-based accessibility can potentially diminish social exclusion rates and improve the well-being of these population groups. This research analyzes the spatio-temporal variability and the socio-demographic characteristics of transit-based job accessibility in Flagstaff, Arizona. This study employs a temporally-enabled schedule-aware simulation based on the transit system's General Transit Feed Specification and the city's street network. Gravity-based measurements were used in the calculation of accessibility from origin locations to job opportunities. This accessibility calculation considers the supply and demand location characteristics, the travel time impedance between them, and temporal variations in transit service frequency and availability. Statistical analyses were used to measure the relationship between accessibility and the individual socioeconomic attributes. The results served as the quantitative basis for discussing the social aspects of the city's transportation system.