Muffled
Jesus in me
Actually there is an indication that Adam couldn't live forever: The Tree of Life.
The Tree of Life was planted there for reason, just as there were reason to plant the Tree of Knowledge there.
If God didn't put the Tree of Life (and no Tree of Knowledge) in Eden, Adam still would have live a long life, but it would have been a life without toil, without suffering, without pain, but he still would have been "mortal".
The narrative in Genesis 2 and 3 made it quite clear that no "living forever" without the fruit from the Tree of Life. So yes, Muffled, there are couple of hints that God didn't make Adam immortal at the very start of creation.
That's quite possible, but it is still speculation.
I believe that is a non-sequitur. Please try to show your reasoning.
I believe you are assuming that Adam could not be created with eternal life. Certainly Christians believe that they will be changed bodily so that they have eternal life when Jesus returns and that does not require the fruit of a tree.
I believe what can be created can also be removed. However I am willing to view it as a creation of dependent eternal life ie dependent on the tree of life. There is no command to Adam to eat of the tree of life, so it does not appear to be that crucial.