The whole of the narrative of Revelation 12 centers on the enmity, hatred, between Satan, the dragon, and the woman. If we apply the relationship of cause and effect we can again place this event after the fall of man.
Enmity
Serpent vs. Snake
There weren't any snakes before the fall of man. It's a logical conclusion which is deduced by the application of cause and effect, logic and reason. Look at it this way, you can’t curse a snake to be limbless, it already is.
July 6th
Hell was prepared, in advance, for Satan and the rebellious angels who were cast out of heaven. However, hell began at the fall of man. This means that it's impossible for Satan to have been in the garden of Eden to beguile Eve.