I am sorry am I missing something here. I swear Sauron HAD made the ring at the time of the downfall. I cant think of a timeline with dates, but i can think up a few quotes, or near quotes that support it.
Quote:
Sauron put on his Fairest form and came to the elves, naming himself Arator [sp?], giver of gifts
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Quote:
His spirit fled, but never again could he apear fair
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The suggestion here is that he must have come to the elves before he lost his ability to apear fair, thus making the Ring first. But i believe he could have survived anyway really, he was a powerful spirit who wouldn't loose that much power through loosing his body.