We investigate dijet production from proton-nucleus collisions at the Large Hadron Collider (LHC) as a means for observing superfast quarks in nuclei with Bjorken \(x>1\). Kinematically, superfast quarks can be identified through directly measurable jet kinematics. Dynamically, their description requires understanding several elusive properties of nuclear QCD, such as nuclear forces at very short distances, as well as medium modification of parton distributions in nuclei. In the present work, we develop a model for nuclear parton distributions at large \(x\) in which the nuclear dynamics at short distance scales are described by two- and three-nucleon short range correlations (SRCs). Nuclear modifications are accounted for using the color screening model, and an improved description of the EMC effect is reached by using a structure function parametrization that includes higher-twist contributions. We apply QCD evolution at the leading order to obtain nuclear parton distributions in the kinematic regime of the LHC, and based on the obtained distributions calculate the cross section for dijet production. We find not only that superfast quarks can be observed at the LHC, but also that they provide sensitivity to the practically unexplored three-nucleon SRCs in nuclei. Additionally, the LHC can extend our knowledge of the EMC effect to large \(Q^2\) where higher-twist effects are negligible.