thanks for this brilliant question
This all depends on where the moon is in its current lunar cycle. At full moon it is exactly opposite the Sun, giving us a very bright moon in the night sky but nothing during the day. As it gets closer to new moon phase the moon is moving closer to the Sun. This makes it less bright at night but more visible during the day.
So that is why we can see the moon during the day. The moon is highly reflective and close to the Earth so it is very visible both day and night. Its orbit increases its visibility because the Moon gets close to the sun towards the beginning of the lunar cycle as travels around the sky.
hope this clear