Question

... Why we would not be able to see the moon without the Sun

Answer 1

Because the light of the sun illuminates the moon's surface. The light then reflects off and travels back to earth. Without the sun, there would be no light rays to bounce back to earth, thus the moon would blend in to space.

Answer 2

There would be no light for the moon to reflect.  We can only see the moon because the sun gives off light, and then that light hits the moon, and bounces back down to Earth (only some of the light).  Then, our eyes receive that light.  Without the sun, there would be no light coming from the sun, and bouncing off the moon.