People seem to think the concept of "unconditional" is permanently wrapped into the concept of "eternal."
One is the quality the other is the quantity—eternal life is quality, living eternally is quantity.
If God said Adam would not die if he did not sin, that is, by definition, offering something eternal.
Now we are getting somewhere.....
Rom 5:12 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:
Death preexisted Adam. It entered this world by sin. However, that doesn't establish the concept (or lack thereof) relative to Eternal Life.
1. Death preexisted Adam
Gen 2:17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.
2. The process of creation was progressive. The first day, second day, third day.......etc.
Gen 1:3 And God said, Let there be light: and there was light.
Gen 1:4 And God saw the light, that it was good: and God divided the light from the darkness.
Gen 1:5 And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.
Where is the concept of Eternal life found in the narrative of Adam and Eve?
The only place we read such a reference deals with keeping man from Eternal life.