I can comfortably say age 3 at launch yes,
A few examples would be Janissaries, Spahi, and the little cannon dudes (I can’t remember their names) for Ottomans
Redcoats, rockets, kings hussars for British
Cossacks, the later iterations of stretsly(forgot their name too) for the Russians
And the Asian dynasties did even more
The Japanese samurai, agashuru musketeers
The Indian elephants, little hand sword dudes
Every civ had at least two unique units, either unlocked by age or via the “guard” upgrades. A lot of them had more, and they usually also each had a special artillery piece of some sort.
Here’s a handy screenshot showing all the launch civs and their respective unique units. - note this is not a complete list, it appears things that are upgrade units and also specials (like redcoats) arent included in this list.
British also had redcoats and kings hussars
Dutch had a special broadsword unit pretty big omission also
Note: swedes weren’t base game, but removing them we still get more at launch that age 4 has
