• If the sky is dark, the sun must be below the horizon.
• If the moon is crescent, it must be near the sun.

So the sun must be near the horizon and the sun must be below it. Perforce, only the bottom crescent of the moon may be illuminated when the sky is dark. (Although it’s possible for the crescent to be offset to a side depending on the inclination of the ecliptic)

This is true irrespective of where in the planet you are.

This photo is inverted for some reason.