Treebeard is at least three ages old, as he relates in the chapter named for him:

>"The trouble is that there are so few of us left... Only three remain of the first Ents that walked the woods before the Darkness: only myself Fangorn, and Finglas and Fladrif- to give them their Elvish names: you may call them Leaflock and Skinbark if you like that better."

According to Gandalf, Treebeard is older than Leaflock and Skinbark, so neither is the first Ent despite their extreme age
>For Treebeard is Fangorn, and the eldest and chief of the Ents, and when you speak with him you will hear the speech of the oldest of all living things.


The Darkness Treebeard referred to was Morgoth, not Sauron, as clarified a little latter. So by first Ents, Treebeard claims to go very far back:

>Then when the Darkness came in the North, the Entwives crossed the Great River... After the Darkness was overthrown the land of the Entwives blossomed rickly and their fields were full of corn. Many men learned the craft of the Entwives and honoured them greatly; but we were a legend to them, a secret in the heart of the forest. Yet here we still are, while all the gardens of the Entwives are wasted: Men call them the Brown Lands now.

>I remember it was long ago-in the time of the war between Sauron and the Men of the Sea-desire came over me to see Fimbrethil again...We crossed the Anduin and came to their land, but found it a desert... 

Information on Ents is pretty rare outside these passages, and no other Ents that might be older than Treebeard are ever mentioned. I'm not sure any passages precludes there being an Ent that was older than Treebeard killed before the events of *the Two Towers* (Fimbrethil could technically be one if Gandalf believes she was dead), but there's no particular reason to assume that either.