M.J.
the fact that they were to die in the "same day" is a matter of debate/interpretation. You know that the Bible says that with God a day is like a thousand years. So God could've very well meant 1,000 years and since Adam and Eve both lived less than 1,000 in God's eyes they did die "on the same day" they ate from the tree. The way I see this is like this: Yes, Adam and Eve were created perfect or sinless however you want to call it. That's made known to us in the Bible by Paul. Obviously, God required Adam's and Eve's obedience to prove they were worthy of being his creatures forever. Now, whether they had knowledge of the "tree of life" prior to God mentioning it, we can't be sure and we also can't be sure whether they ate of it but that's contingent upon them knowing about its existence. We know that as long as they were sinless, they were not to die. They may not have been given eternal life at the time of creation but there was nothing or no one that could kill them. Take Jesus for example. He was perfect and sinless. Had he not been killed, he would've never died since he wasn't affected by sickness and death like we all are. But it doesn't mean he couldn't have been killed. And we know he was. But Adam and Eve were alone and nothing threatened their existence. If Satan had decided to kill them, God could've well intervened or given them their life back because they died without sinning or without it being their fault.
Anyway, like I said, there's no hint in the Bible that they knew of the tree of life prior to God mentioning it. God only told them to "eat from every tree in the Garden" and forbade them to eat from just one. Just because the "tree of life" was in the Garden, doesn't mean they ate from it. There were many other trees. Gen. 3:9 says: Thus Jehovah God made to grow out of the ground every tree desirable to one’s sight and good for food and also the tree of life in the middle of the garden and the tree of the knowledge of good and bad. Notice that after mentioning "every tree... good for food", the Bible says AND "also the tree of life... and the tree of the knowledge of good and bad." It could be understood as the last two trees not being for food and God only told Adam about the "tree of knowledge of good and bad". So again, Adam and Eve probably didn't know about the tree of life. Whether they ate from it without their knowledge of it being "the tree of life" had no bearing on their continue living. They didn't need it to keep living since they were sinless and only needed food to sustain them. In other words, the "tree of life" was not a life-sustaining tree. It probably was there just as a tangible and physical sign/proof/evidence that once God thought Adam and Eve had proven faithful and obedient, he would tell them about it and tell them to eat. Again, it probably had no "magic powers" but if Adam and Eve ate from it at God's command and believed they would live forever because they ate from the tree, and then it showed faith on their part. The "tree of knowledge of good and bad" had no magical powers either. It didn't take away their perfection or sin. It was the ACT of them disobeying God that brought their demise, not the tree itself.
Justahuman - but super nonetheless