We reconstruct all (2+1)D quantum double models of finite groups from their boundary symmetries through the repeated application of a gauging procedure, extending the existing construction for abelian groups. We employ the recently proposed categorical gauging framework, based on matrix product operators (MPOs), to derive the appropriate gauging procedure for the $\mathsf{Rep}\, G$ symmetries appearing in our construction and give an explicit description of the dual emergent $G$ symmetry, which is our main technical contribution. Furthermore, we relate the possible gapped boundaries of the quantum double models to the quantum phases of the one-dimensional input state to the iterated gauging procedure. Finally, we propose a gauging procedure for 1-form $\mathsf{Rep}\, G$ symmetries on a two-dimensional lattice and use it to extend our results to the construction of (3+1)D quantum doubles models through the iterative gauging of (2+1)-dimensional symmetries.
