That's not how I read the bible.
What I find intriguing is that God told Adam and Eve that if they sinned they would die and return again to the dust they were made from:
Gen 3:19 In the sweat of thy face shalt thou eat bread, till thou return unto the ground; for out of it wast thou taken: for dust thou art, and unto dust shalt thou return.
It says absolutely nothing about their souls living on in immortality.
What's really fascinating is that this idea is first broached by Satan:
Gen 3:3 But of the fruit of the tree which is in the midst of the garden, God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die.
Gen 3:4 And the serpent said unto the woman, Ye shall not surely die:
God says we will surely die. Satan says we will surely not. Who to believe? :-)