When were the Ents born......

[Elrian]

Here is how Ents came into being in the First Age: from The Silmarillion.

Then Manwe awoke, and went down to Yavannah upon Ezellohar, and sat beside her beneath the Two Trees. And
Manwe said; O Kementari, Eru hath spoken, saying: "Do then any of the Valar suppose that I did not hear all the Song, even the least sound of the least voice? Behold! When the children awake, then the thought of Yavannah will awake also, and it will summon spirits from afar, and they will go among the kelvar. and the olvar, and some will dwell therein, and be held in reverence, and their just anger shall be feared.

Olvar means growing things with roots in the earth. Kelvar is animals; living things that move.