This came up because a friend told me he thought Glorfindel was an "original elf". As far as I know, the earliest mention of Glorfindel is at the Fall Of Gondolin, which is a far cry from Cuiviénen.
Elu Thingol is certainly old enough to have been at Cuiviénen, but he had brothers Olwe and Elmo, which would seem to disqualify him from awakening. If he considers all the original elves to be siblings, why single out those two, and why exclude Finwe from that distinction?
Finwe and Círdan are the best candidates I can think of, but I can't recall if their origin was ever specifically stated.