There’s absolutely no way that could have happened. While Sauron was defeated on the slopes of Orodruin, the movie scene where Isildur and Elrond climb to the ledge of the fires isn’t in the books.

Elrond recounts what happened that day to Boromir, much later:

Isildur took it, as should not have been. It should have been cast then into Orodruin’s fire nigh at hand where it was made. But few marked what Isildur did. He alone stood by his father in that last mortal contest; and by Gil-galad only Círdan stood, and I. But Isildur would not listen to our counsel.

‘“This I will have as weregild for my father, and my brother,” he said; and therefore whether we would or no, he took it to treasure it. But soon he was betrayed by it to his death; and so it is named in the North Isildur’s Bane. Yet death maybe was better than what else might have befallen him.

There’s no way Elrond could have picked up a grieving Isildur who is holding his dead father, carried him kicking and screaming, and yeeted him off the precipice.

Imagine, in the hour of such a pyrrhic victory, with Gil’galad and Elendil bodies still warm after their sacrifice, trying to murder the new High King of the Dúnedain and, technically, the ruler of both Arnor and Gondor over having claimed a ring? That’s a whole new war right there between what human and elven armies were still standing…