before Adam sinned, there was no death in him, because death only enters through sin.
so Adam did have eternal life - it wasn't something he had to 'attain' - but something he lost when he added death to himself by sin.
Romans 5:12
Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned
this isn't the same as the eternal life given to him, and to us through Christ, because we now have sin atoned for.
Adam had life without sin, and the freedom to reject it. after he sinned, we all have death with sin, and the freedom to receive life through the promise of God, the finished redemptive work of the Son.