so...the reason Adam later died of old age is due to his sin, thats for sure.
But specifically he died because he was unable to eat of the tree of life.
The tree of life gives eternal life to a mortal man that eats of it...
What mortal man is there in the story?......only Adam.
The fact that God planted the Tree of Life in the garden in the first place proves 100% that God created Adam as a mortal.