It is established that Mount Doom is the only practical possibility. LOTR I.2 (when Gandalf verifies that Frodo's ring is the Ring and tells Frodo what that means):
But there is no smith's forge in this Shire that could change it at all. Not even the anvils and furnaces of the Dwarves could do that. It has been said that dragon-fire could melt and consume the Rings of Power, but there is not now any dragon left on earth in which the old fire is hot enough; nor was there ever any dragon, not even Ancalagon the Black, who could have harmed the One Ring, the Ruling Ring, for that was made by Sauron himself. There is only one way: to find the Cracks of Doom in the depths of Orodruin, the Fire-mountain, and cast the Ring in there.
(Several of the Seven were destroyed by dragons.)
Ways to destroy the Ring are discussed in Rivendell (LOTR II.3). When Tom Bombadil is suggested, Gandalf states
Say rather that the Ring has no power over him. He is his own master. But he cannot alter the Ring itself, nor break its power over others.
It is not said in this discussion whether the Valar, or other powers in Valinor, may be able to destroy the Ring. Quite possibly, they could, but will not.
‘But Gandalf has revealed to us that we cannot destroy it by any craft that we here possess,’ said Elrond. ‘And they who dwell beyond the Sea would not receive it: for good or ill it belongs to Middle-earth; it is for us who still dwell here to deal with it.’
My understanding is that there is no magic in Middle-earth that is strong enough to destroy the One Ring, and there is but one natural method to destroy it which is to melt it in a volcano. The fact that the Ring was made in Mount Doom is not directly relevant: Mount Doom is the only volcano mentioned in the story (not explicitly, but “Fire-mountain” is transparent). I don't have any hard in-story or out-of-story evidence to show, however.