There have been limited studies linking baseline factors, including the viral load (VL) test, with virological non-suppression since the introduction of dolutegravir (DTG)-based regimens as first-line antiretroviral treatment (ART) in Ethiopia. This study aimed to identify baseline factors associated with virological non-suppression between October 2020 and July 2022. A follow-up study was conducted in eastern Ethiopia among newly diagnosed people living with HIV (PLHIV). A questionnaire and a checklist were used to collect the data. Five milliliters of venous blood were obtained at baseline and six months to determine the VL. A VL test was performed using the Abbott RealTime HIV-1 assay. To determine predictors of virological non-suppression, bivariate and multivariate logistic regression analyses were used. There were 235 PLHIV enrolled, 70.6% of whom were female, with a mean age of 33.9 years. Of the 161 retained on ART, virological non-suppression was 8.7% at six months. Baseline predictors of virological non-suppression were age ≤ 30 years, a history of substance use, and a VL greater than 4-log10 copies/mL. In this cohort, virological non-suppression was found to be optimal but still lagged slightly behind the third 95%–target. Thus, targeted interventions, the introduction of baseline VL testing to improve treatment outcomes, and fostering the attainment of UNAIDS 95–95–95 targets are recommended. Furthermore, broader research is recommended to explore the reasons for virological non-suppression in the study area.