My understanding of ring lore is that Sauron, disguised as Annatar, Lord of Gifts, taught Celebrimbor and the elves of Eregion how to make rings of power, and together they made the Seven and the Nine. But they were tainted with Sauron's influence and Celebrimbor began to suspect Annatar. So he made the Three by himself, in secret and without Annatar's guidance, (as referenced in this answer here, though the text has been removed from the source Wiki article), and Sauron made the One in secret too. When he put on the One Ring, Sauron and the bearers of Three sensed each other, the elves knew Annatar for Sauron, and the elves removed the Three and hid them.
But the One Ring bears the infamous inscription:
Three Rings for the Elven-kings under the sky,
Seven for the Dwarf-lords in their halls of stone,
Nine for Mortal Men doomed to die,
One for the Dark Lord on his dark throne
In the Land of Mordor where the Shadows lie.
One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them
In the Land of Mordor where the Shadows lie.
The One Ring must have been forged with this inscription, right? So how did Sauron learn about the existence of the Three before he forged the One?
EDIT: I answered this myself when I realized the verse is not on the ring, only the couplet
One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them
So if I may modify my question: Is there any evidence that he did know of the Three before he put on the ring?