In “Of Aulë and Yavanna” this is said: “Behold! When the Children awake, the the thoughts of Yavanna will awake also, and it will summon spirits from afar, and they will be among the kelvar (animals) and olvar (plants), and some will dwell therein, and beheld in reverence, and their just anger shall be feared. For a time while the firstborn are in power, and while the secondborn are young.”
So this suggests at least after the elves, the ents were awakened. Círdan was a Teleri elf from Cuiviénen who did not go to Valinor. This statement also suggests the ents were awakened after Men, so maybe early FA.
Either way, I’m going to lean Círdan, because the firstborn are first for a reason, that being said, Círdan has barely any representation in the films, so maybe Treebeard.