If Adam and Eve hadn't sinned, would they have remained on earth forever?

I’ve been wondering how to reconcile the idea that human death is a punishment for original sin with the observation that everything that is alive eventually dies. I know that if God wanted to grant humanity with eternal life and stay on earth, he could easily do that, but wouldn’t that eventually overpopulate the earth if no one died? Also, aren’t we supposed to want to be with God, and not stay on earth?

I’ve come up with a tentative solution, which makes sense to me at least, that would explain this. In their unfallen state, humans might have simply chosen to die and then be assumed into heaven. My evidence for this is Mary, who died and assumed into heaven, since she actually was in an unfallen state. Scripture also points to the idea of assumption, since Enoch and Elijah were taken body and soul by God (though obviously, since they were born with original sin, they couldn’t go directly to heaven).

So I’d like to know, is this solution acceptable doctrinally, and if not, what is the Church’s solution?

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Was there death before the Fall?

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