Do you always watch well?
Have a look on the sky at daytime also and you will see the moon. Why? Because it is always there just like the stars but the difference is that the stars’ light is very few comparing to the moon’s.
You can see the moon only because it reflects the light coming from the sun. You cant see the whole globe moon because only the lit part of it can be seen. Have a look on it at the daytime and you will see that the seeable part if looking to the sun.
Did you know that the moon is much further than many people think? Apollo missions had to travel 3 days to the moon. If you would say that is nothing, just imagine how far from the Earth you could travel with a normal plane with 3 day traveling. BUT the difference is that as there is no atmosphere in the space, there is no hypersonic speed also (which the reason is for the planes on Earth not going faster than around 1000 km/h) so they travel much much much much faster than a usual aeroplane. And still it takes 3 days to arrive. Moon is not our neighbor actually. Just the closest.