Sunrise

When she judged that Odysseus had taken sufficient pleasure from mingling with his wife, and from sleep itself, she immediately roused from Ocean early-born golden-throwned Dawn, who brings light to men.

'Athena' watched over them:

Odyssey Book 23 line 307-310 Barry B Powell
Odyssey Book 23 line 322-324 Barry B Powell
Odyssey Book 24 line 373-375 Barry B Powell

Winter Solstice over the foot Mount Neion seen from Pyrgi

Meaning Odysseus didn't make it late, there is another trail ahead, first step is fleeing the Achaeans! And Odysseus has made himself a plan.

...Rumor, the messenger, went swiftly everywhere though the city, telling of the awful death and fate of the suitors. The people heard it all at once and gathered from every corner,

Right away, at the time of the rising sun, a report about the suitors I killed will get out. You go up to your upper chamber with your attendants and wait there. Look on no man and ask no questions.

Odysseus has set a distraction for all of the Achaeans. You already know the story of Rumor.

Here is the story of Rumor again. Earlier we came to the conclusion that the people must have been gathered first before Rumor told them the message all at once. And of course it was meant to gather to people for the first sunrise of the new year in Pyrgi, welcoming a new cycle of the sun.

Sunrise at winter solstice would be somewhere over mount Neion. To find out where that exactly would be I went there in December 2021. Since the mountain reaches high in the sky, there is plenty of daylight for Rumor to gather all the people in time to observe the sunrise at Pyrgi.
And then tell them.

All the people were already gathered there awaiting the first sunrise of the year, and Rumor was able to tell the people all at once that Odysseus had killed all of the suitors in the palace.