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When I got to the city the late afternoon traffic had started to appear.

How can I describe this in a satisfying way? (I don't want it to sound like there was no traffic before, because there's always traffic in a city.)

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When I got to the city the late afternoon traffic had started to appear. This is not wrong.

You could also say

eg When I got to the city, the late afternoon traffic had started to build up.

eg When I got to the city, the late afternoon rush hour traffic had started.