An individual's risk of substance use disorder (SUD) is shaped by a complex interplay of potent biosocial factors. Current neurodevelopmental models posit vulnerability to SUD in youth is due to an overreactive reward system and reduced inhibitory control. Having a family history of SUD is a particularly strong risk factor, yet few studies have explored its impact on brain function and structure prior to substance exposure. Herein, we utilized a network control theory approach to quantify sex-specific differences in brain activity dynamics in youth with and without a family history of SUD, drawn from a large cohort of substance-naïve youth from the Adolescent Brain Cognitive Development Study. We summarize brain dynamics by calculating transition energy, which probes the ease with which a whole brain, region or network drives the brain towards a specific spatial pattern of activation (i.e., brain state). Our findings reveal that a family history of SUD is associated with alterations in the brain's dynamics wherein: i) independent of sex, certain regions' transition energies are higher in those with a family history of SUD and ii) there exist sex-specific differences in SUD family history groups at multiple levels of transition energy (global, network, and regional). Family history-by-sex effects reveal that energetic demand is increased in females with a family history of SUD and decreased in males with a family history of SUD, compared to their same-sex counterparts with no SUD family history. Specifically, we localize these effects to higher energetic demands of the default mode network in females with a family history of SUD and lower energetic demands of attention networks in males with a family history of SUD. These results suggest a family history of SUD may increase reward saliency in males and decrease efficiency of top-down inhibitory control in females. This work could be used to inform personalized intervention strategies that may target differing cognitive mechanisms that predispose individuals to the development of SUD.