Is it possible to completely see the edge of a half moon at night?
As uhoh has written in the comments, this phenomenon is known as &quot;planetshine&quot;, and in this case more specifically &quot;earthshine&quot;. The sunlight hits the earth and is reflected to the moon, illuminating what cannot be directly reached by the sunlight.

https://en.wikipedia.org/wiki/Planetshine
https://en.wikipedia.org/wiki/Earthlight_(astronomy)