If you look up at the sky right after sunrise, you might be able to see the moon in a clear morning. Such a phenomenon usually happens after the full moon and will persist until the new moon.
In the days after full moon, the moon is officially in a waning gibbous phase, rising after nightfall and setting in a westward direction shortly after sunrise. If you look for the moon at the same time every morning, you’ll see this week’s waning moon appearing higher and higher in the western sky each early morning, for several days.
Though I won't be seeing the daytime moon anytime soon, I have been able to see it before. I was curious why I saw the moon in the day. Now, I understand the reason behind it. For others, they might know this type of moon as the "children's moon" with varying explanations as to why it's called that way. We will see the daytime moon until August 1, when the moon becomes new again.
(Image credit: Robert Kixmiller/Wikimedia Commons)
Perhaps people don't notice it because it's not bright enough to attract their attention?