If we set the date to somewhere close to 10,500 BC, then if we chose the time of day so that Regulus that Bauval proposed corresponds to the sphinx is on the horizon, then the orientation of the Orion belt stars agree with that of the pyramids. The year would have to be fine tuned though.
But there is a problem with this idea. It is that of intent. If the architects had this in mind then surely they would have encoded the exact position - direction of Regulus. Turns out they didn't. Both the direction of its body as also that in regards to the central pyramid do not match.