According to biblical source they were made in God's image and immortal. Their punishment was mortality and expulsion.

Today science finds that aging is like a very slow disease. It's why many believe aging can be "cured" to various degrees. We also know that some animals don't die from old age. These simply die from predation.

Science says it's at least plausible.

We don't know about how "immortal" Adam and Eve were, but the tree of life was in the garden with them, and they were permitted to eat from it (but didn't get around to it) which is why they ended up getting kicked out after eating from the tree of knowledge.