Maybe..
The biblical notion that the world's first city is founded by Cain, is recalling Gilgamesh who lives at Sumerian Unug (Babylonian Uruk), Unug being recast as Enoch.
But Uruk isn't the oldest city in the world. It is ancient, but by no mean the earliest.
Damascus and Jericho are older still, by several thousand of years.
Like Uruk, Jericho was successively built on top of older layers of settlements.
The oldest layer of Jericho is about 12,000 years old (hence around 10,000 BCE), which was among the earliest Neolithic village.
What is really amazing about Jericho is that there were no pottery this early in the Neolithic period, and yet they were advanced enough to construct homes make from sun-dried clay and straw bricks, about a thousand years later, construct the stone walls around the town, and even a tower with stairway!
Jericho is oddity, because when Jericho was abandoned almost 1000 years later, you would expect the newer town would be more advanced and city would be larger than the old. Instead the immediate newer town was smaller in size with no fortified walls. Technology, they were less advanced, probably due to the residents being invaders.
Jericho would not become a walled city until the Bronze Age (around 25-2400 BCE).
Like Jericho and Uruk, Damascus was a city of long history, but its earliest city was no where as advanced as Jericho in the 9th millennium BCE. Damascus wan't prominent until the late Chalolithic period (when people were using copper tools as well as stone, the Chalolithic period started around 4000 BCE, and its more like transitional period between Neolithic and Bronze Age).
Another city, a Phoenician city, I can't remember if it was Byblos or Sidon (goodness, my memory seemed to be slipping), is about roughly the same age as Uruk, but whichever one it is, the city didn't become a seafaring city-state until the Bronze Age.
No, sooda, Uruk isn't the first or oldest city. Uruk wasn't important until 4200 BCE, and reaching its zenith around 3600 to 2900 BCE. Gilgamesh, belonging to the 1st dynasty of Uruk, was said flourished around 27th or 26th century BCE, but we know from legend and myth than the historical Gilgamesh.