The neshama was not destroyed in the Fall, Adamic men were destroyed in the Flood (except for Noah et al):
'aph n@shamah ruwach chay charabah muwth
I didn't say destroyed...I said corrupted. Man became a deaf and blind mute and even though creation screamed the true God man could only sense the vibrations of the true God and he conjured up all sorts of fantasies in his own mind, conflating the creation with the Creator.