In this work, we characterize cofinal functors of (∞, 2)-categories via generalizations of the conditions of Quillen's Theorem A. In a special case, our main result recovers Joyal's well-known characterization of cofinal functors of (∞, 1)-categories. As a stepping stone to the proof of this characterization, we use the theory of 2-Cartesian fibrations developed in previous work to provide an (∞, 2)-categorical Grothendieck construction. Given a scaled simplicial set S we construct a 2-categorical version of Lurie's straightening-unstraightening adjunction, thereby furnishing an equivalence between the ∞-bicategory of 2-Cartesian fibrations over S and the ∞-bicategory of contravariant functors Sop →𝔹icat∞ with values in the ∞-bicategory of ∞-bicategories.