  The central super-massive 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
${\sim}10^{-3}\rm\ M_{\odot}\ yr^{-1}$ 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 (${\sim}10^4\rm\ K$) in its vicinity raised
questions about how such material could settle in the hostile (${\sim}10^7\rm\
K$) 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 ${\sim}500\rm\ yr$ with material being captured at a rate of
${\sim}10^{-6}\rm\ M_{\odot}\ yr^{-1}$ at scales of ${\sim}10^{-4}\rm\ pc$,
consistent with the observations and previous models. However, on longer
timescales ($\gtrsim3000\rm\ yr$) the material accumulates close to the black
hole in the form of a disk. Considering the duration of the Wolf-Rayet phase
(${\sim}10^5\rm\ yr$), we conclude that this scenario likely has 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.
