Multidisciplinary care with free, rapid, and on-site bictegravir/emtricitabine/tenofovir alafenamide (B/F/TAF) dispensation may improve health outcomes among migrants living with HIV. However, models for rapid B/F/TAF initiation are not well studied among migrants living with HIV, and an understanding of how social determinants of health (SDH) may affect HIV-related health outcomes for migrants enrolled in such care models is limited. Within a 96-week pilot feasibility prospective cohort study at a multidisciplinary HIV clinic, participants received free B/F/TAF rapidly after care linkage. The effects of SDH (i.e., birth region, sexual orientation, living status, education, employment, French proficiency, health coverage, use of a public health facility outside our clinic for free blood tests, and time in Canada) and other covariates (i.e., age, sex) on median time to antiretroviral therapy (ART) initiation and HIV viral undetectability from care linkage were calculated via survival analyses. Thirty-five migrants were enrolled in this study. Median time to ART initiation and HIV undetectability was 5 days (range 0-50) and 57 days (range 5-365), respectively. Those who took significantly longer to initiate ART were aged <35 years, identified as heterosexual, had less than university-level education, or were unemployed. No factor was found to significantly affect time to undetectability. Despite the provision of free B/F/TAF, several SDH were linked to delays in ART initiation. However, once initiated and engaged, migrants living with HIV reached HIV undetectability efficiently. Findings provide preliminary support for adopting this care model with migrants living with HIV and suggest that SDH should be considered when designing clinical interventions for more equitable outcomes.