Isn't Solar System in technical reach of current tech from Sirius Sector? If I remember right, the jumpdrives from Starlancer were "slow" enough to make it a great deal for warships to cross Solar System in matter of long days, if not weeks. It is pretty likely that the Sleeper Ships used the exact same tech to arrive into Sirius Systems so it cannot really be that far.
Also, it is worth to mention, if believe the FL Nomad Legacy being in 80% reproduction of Freelancer Alpha, there was actual Sirius, meaning the initial idea of Sirius Sector wasn't that far from Sol.
P.S. Freelancer Extended Intro is canon for Discovery. It means that there's nothing much left in Solar System, except for radiation, planetary remains and Pluto.