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 ∼10−3 Me 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 (∼104 K) in its vicinity raised questions about how such material could settle in the hostile (∼107 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 ∼500 yr with material being captured at a rate of ∼10−6 Me yr−1 at scales of ∼10−4 pc, consistent with the observations and previous models. However, on longer timescales (≿3000 yr) the material accumulates close to the black hole in the form of a disk. Considering the duration of the Wolf–Rayet phase (∼105 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.