Is there a point in history from which we can say that, from this date forward, there has always been at least one person in space? If so, what is that date?
The last crew on Mir came back on June 16, 2000, and the first ISS crew launched on October 31, 2000. So I think the answer is October 31, 2000.
The International Space Station has been continually staffed since November 2, 2000.
The first crew came to the ISS on a mission called Expedition 1, which launched on October 31, 2000, so it would seem that October 31, 2000 is the date you’re after.
When they got to the station, did they do the Smurf?
If you’re curious, according to this list of Mir missions there was someone on board Mir (or travelling to or from it) from September 5, 1989 until August 28, 1999 — eight days shy of ten years. (The last Mir crew didn’t overlap with the second-to-last; it seems that the station was unoccupied for seven months.) I believe this is the longest sustained period (so far) that there has been someone in space.
If Wikipedia is to be believed, the Shuttle was up from October 11, 2000 until about October 23. But for a few days’ gap, it almost pushed the date back a few weeks.