You mkae an essential point. Ponder the following, if you will: God’s Spirit IS eternal life.. In Adam the Spirit of God was upon Adam and Eve, like a shawl, not in their spirit but upon their spirits. With the fall of mankind, the Spirit left the spirit presence in the first family. BUT GOD had a plan to put His Spirit IN the spirit of whomever of Adam’s descendants would ask for deliverance from the sin nature they inherited from Adam the progenitor. The human spirit that has His seed ABIDING in it (1 John 3:9) is alive forever more because it is God Who is in them, in their once dedness residing spirit.
Death was introduced, not being inevitable unless man sinned:
Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: (Romans 5:12)
For if by one man’s offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ.) (Romans 5:17)
'It's easier to fool people than to convince them that they have been fooled.'
-- Mark Twain
Adam was always subject to death. Immortality cannot be tempory.
You know this how?