(1) Background: The main goal of this study was to analyze the HIV epidemic temporally and spatially among young people living in Pará, Brazil, from 2007 to 2018; (2) Methods: For the temporal analysis, we employed an integrated autoregression of moving averages model associated with the seasonal trend using the LOESS decomposition method, which allowed for predictions to be made. In the spatial analysis, the techniques of autocorrelation, spatial and spatio-temporal risk analysis, and geographically weighted regression were used; (3) Results: During the study period, there were 8143 notifications of HIV/AIDS cases. The temporal prediction indicated a trend of growth in the incidence rate in the 20–24-year-old group from January 2019 to December 2022 and a trend of stability in the 15- to 19-year-old and 25- to 29-year-old groups. There was a territorial expansion of the HIV epidemic in Pará. Novo Progresso and the Metropolitan Region of Belém (RMB) were the zones with the highest spatial and spatio-temporal risk for HIV. Social determinants including the Basic Education Development Index, the number of physicians per 10,000 inhabitants, and the municipal high school abandonment rate in the municipalities were associated with the risk of HIV/AIDS among young people in Pará; (4) Conclusions: To eliminate HIV among young people in Pará, the access to treatment, diagnosis, and preventive healthcare services should be expanded. Sexual and reproductive health education should be reinforced in schools and communities. Furthermore, it is necessary to promote social equity and fight HIV stigma.