[Ivriniel]

So....by this account (for version I of the deliberately dual text), Olorin was a pre-Istari visitor bearing a returned gift by the Grace of Yavanna. Galadriel was a jaded, cross, Elf, tossed out of the Ost-In-Edhil, by naughty Elfs, who spent too much time, hangin' out with Annatar the resident bad boi.

The Olorin-out-of-the-West is a theoretical possibility.

However, I found another reason to presuppose Version 1 is not the "one only the wise knew" (UT put it that way). UT notes that The Elessar made a region in Beleriand heal (like Vilya did) with Enerdhil's jewell, before it passed into the West. The Silmarillion then goes onto apply a Silmaril (i.e. not the Elessar) as the basis for this 'healing' before it left Beleriand.

Further, in Version II, we're told the second Elessar had less joo joo. The first Elessar could make a whole region grow Valinorish (ie. was Vilya-ish). The second Elessar, though "more subtle" and "clearer" than the first, could not imprison light from the sun when she was 'young'. Morgoth's influence from the Void.

I didn't see Aragorn's Elessar doin' very much joo joo and so, this places it more as the Celebrimbor/Feanorean jewel.