[nurtbo]

The aughts or naughts (or aughties) are a pretty easy to understand way to refer to 2000-2009, though saying “the early aughts” is clearly more verbose than saying 2000-2003 (except that 2000-2003 looks more specific than is meant)

[kelnos]

I think that last point, "there’s no good way to refer to 2000-2009, sorry", was a bit tongue in cheek, refusing to acknowledge "the aughts", since it is a terrible, terrible, stupid way to refer to anything.