As much as we associate the Moon with night, you certainly have seen it during the daytime.
Yesterday, the Moon was in a waning gibbous phase and I saw it in the light of morning. During this phase, it rises in the east later than it did the night before and it will rise later and later each evening. That means you can catch the daytime moon over your western horizon after sunrise now.
The daytime moon is a nice reminder that or favorite natural satellite is up there much of the time. It is pretty pale against the blue sky, so not as noticeable as at night. Our Moon is there during the day half the time since it orbits the entire Earth once a month. It is difficult to see the crescent moon in the daytime because it is near the sun in the sky.
We always notice the Full Moon that stays out all night long, rising at sunset and setting at sunrise. Following Full Moons (the last one was Tuesday) the waning gibbous moon is rising later each night and setting in the west later each day after sunrise.