The 3D distribution of dust and gas in the Milky Way's Central Molecular Zone (CMZ) is key to understanding gas inflows toward the Galactic Centre (GC), the process of star formation in this extreme environment, and the propagation of energetic cosmic rays originating from Sgr A*. However, while recent efforts have combined datasets in a Bayesian framework to estimate the near/far positions of individual molecular clouds in the CMZ, conflicts between different methodologies still remain and we are still lacking a comprehensive, model-independent map of all of the gas and dust in the CMZ, which is critical to address key science questions. Here we develop a new methodology to infer the 3D dust distribution of the CMZ. The key idea of the method is to use stellar proper motions to get probabilistic information about the unknown stellar distances through a model of the distribution of star positions and velocities of the nuclear stellar disc (NSD), co-spatial to the CMZ. Taking stellar proper motions and extinctions as input, the latter adopted as a proxy of the dust column density, the method returns the 3D dust distribution. It is non parametric, makes no a-priori assumption on the dust distribution, and is fundamentally distinct and largely independent of all existing methods. We show that the method can robustly and effectively reconstruct the mock 3D CMZ structure by testing it on a range of mock dust distributions, both analytically generated and taken from hydrodynamical simulations. Finally, we discuss the prospects for applying the method to real data.