How is the moon visible when it is visually blocked by the Earth?

I know this sounds like an incredibly stupid question but I’ve read several links about the orbits of bodies in our solar system, looked at 3d models, and for the life of me I can’t understand how there isn’t a point in the moon’s orbit where it is completely not visible. I know it’s *almost* not visible during a new moon, but there’s still a sliver visible to the naked eye.

I made [this illustration](https://i.imgur.com/ZbaTwqI.png) to show what I mean. How is a person standing at point A able to see the moon?

Not once in my life do I remember a time when the moon was not visible in the night sky (North America). If the Earth orbits the sun, and the moon orbits Earth (as well as the sun obviously), why is there not a point where the moon is in between the Earth and the Sun, and thus people on the side of the Earth facing neither are in darkness and unable to see the moon?