Gas accreting onto supermassive black holes that sit at the centres of galaxies fuels the most powerful engines in the universe, Active Galactic Nuclei, shaping the formation and evolution of their host galaxies. Yet, we have a poor understanding of how the gas is transported from typical galactic radii, R=several kpc, down to the area of influence of the black holes, less than a few pc. The centre of the Milky Way can be studied in much greater detail than any other galactic nucleus and is a Rosetta Stone to understand the physical processes that occur in all galaxies. Interstellar gas is transported from the Galactic Disc down to the central black hole SgrA* through a sequence of steps. The Galactic Bar performs the first step by efficiently transporting gas from the Disc (R=3kpc) down to the ring-like accumulation of gas known as the Central Molecular Zone (CMZ) at R=120pc. In the last few years I have led major theoretical efforts to understand and quantify this first step. However, these efforts have also demonstrated that the bar is ineffective in driving the gas further inwards. A long-standing question is how the gas continues from the CMZ to SgrA*. For the first time we have the possibility to answer this question thanks to new datasets and advances in numerical simulations. I propose here an unprecedented effort to solve this important problem through a unified analysis of all the relevant physical processes based on novel data and methodologies. I will combine recent and upcoming high-resolution astrometric and spectroscopic data with advanced stellar dynamical models to constrain the gravitational potential in the Galactic centre (GC). I will then use this potential to run cutting-edge numerical simulations to systematically quantify the contribution of all the mechanisms that can drive inward mass transport. This will solve the problem of the inward mass transport in the GC and will give us fundamental insights that can be applied to all galaxies.