Let me see what i can take out of the novel…

The exact time is not stated but we can more or less guess.

Rou was in his 20 when he was selected for the rebirth project, and he says the war was happened when he was born.

It was summer, and I had just turned twenty when I was chosen as a core member of the rebirth project.

When I was born, this planet was already in the midst of danger. Due to numerous wars, pollution, and environmental destruction, over half of the territory on earth had been devastated to the point of becoming inhabitable for human life.

(from vol 6 ch 5)

We don’t know how long it took for no.6 to became how it was now (the wall) from the start of the project, but the built of the wall was a slow process: in the time between Shion’s birth (2001 - and his father’s run from no.6 - remember he was a rebirth project member and he already sensed danger) and Mao’s massacre (2005) the wall become what it was now.

“I didn’t know, either,” Rikiga said. “I was already kicked out when they started building it. A massacre, huh… which means No. 6 must have invaded the Mao area and tried to wipe out its residents?”

(ch4vol9)

During Mao massacre he was still in no.6.

We have West Block “still a decent city” 20 years before (said by Nezumi about the map given to Inukashi to search for Rikiga at the beginning).

Than we have Karan’s supposed age: according to this piece

 In No. 6, those under forty years of age consisted the majority of the age demographic. It was a young city. Because of this, the odd elderly person she passed on the street stood out all the more sorely.

(ch2vol3)

we can suppose she’s not 40 yet. Let’s say she is 35, she must have got Shion in her 19, still a possible age.

Now, it’s stated that Karan e Rou had several years of difference:

“Karan and I were childhood friends. I was much older than her, but we often played together.

(vol6ch5)

And that Karan was still a student when she went to meet Rikiga (so 16-18?),

“It was taken decades ago, not long after we met each other. Karan was still a student, and she was interested in the columns I wrote, and came to visit me.”

(ch3vol2)

at that time Rou was already a researcher (was in the photo and presentet as such), so he had finished college or whatever specialization they had.

Let’s say he was 23-25 than? and Karan in her 16 (so, let’s say in 2017 she’s now 35, so in her 16 it was 1998)…. 

If in 1998 Rou was 25, he was born in 1973, in which the war was already exploded.

Please don’t assume my counts for correct, they are just suppositions, and probably i’m forgetting something.