The central supermassive black hole of the Milky Way, Sgr A*, accretes at a very low rate making it a very underluminous galactic nucleus. Despite the tens of Wolf-Rayet stars present within the inner parsec supplying similar to 10(-3) M yr(-1) in stellar winds, only a negligible fraction of this material (<10(-4)) ends up being accreted onto Sgr A*. The recent discovery of cold gas (similar to 10(4) K) in its vicinity raised questions about how such material could settle in the hostile (similar to 10(7) K) environment near Sgr A*. In this work we show that the system of mass-losing stars blowing winds can naturally account for both the hot, inefficient accretion flow, as well as the formation of a cold disk-like structure. We run hydrodynamical simulations using the grid-based code Ramses starting as early in the past as possible to observe the state of the system at the present time. Our results show that the system reaches a quasi-steady state in about similar to 500 yr with material being captured at a rate of similar to 10(-6) M yr(-1) at scales of similar to 10(-4) pc, consistent with the observations and previous models. However, on longer timescales (greater than or similar to 3000 yr) the material accumulates close to the black hole in the form of a disk. Considering the duration of the Wolf-Rayet phase (similar to 10(5) yr), we conclude that this scenario has likely already happened, and could be responsible for the more active past of Sgr A*, and/or its current outflow. We argue that the hypothesis of the mass-losing stars being the main regulator of the activity of the black hole deserves further consideration.