Integrase strand transfer inhibitors (INSTI) are a main component of the current antiretroviral regimens recommended for treatment of HIV infection. However, little is known about the impact of INSTI on neurocognition and neuroimaging. We developed a prospective observational trial to evaluate the effects of INSTI-based antiretroviral therapy on comprehensive brain outcomes (cognitive, functional, and imaging) according to the time since HIV-1 acquisition. We recruited men living with HIV who initiated antiretroviral therapy with INSTI < 3 months since the estimated date of HIV-1 acquisition (n = 12) and > 6 months since estimated date of HIV-1 acquisition (n = 15). We also recruited a group of matched seronegative individuals (n = 15). Assessments were performed at baseline (before initiation of therapy in HIV arms) and at weeks 4 and 48. Baseline cognitive functioning was comparable between the arms. At week 48, we did not find cognitive differences between starting therapy with INSTI earlier than 3 months or later than 6 months after acquisition of HIV-1 infection. Functional status was poorer in individuals diagnosed earlier. This effect recovered 48 weeks after initiation of therapy. Regarding brain imaging, we found that men living with HIV initiating antiretroviral therapy later experienced a greater decrease in medial orbitofrontal cortex over time, with expected negative repercussions for decision-making tasks.