Up until around mid-19th century or so, they were rare in US cities too. If you saw a squirrel in the city it was probably someone's pet. According to a newspaper account from 1856 New York, hundreds of people gathered around a tree that an escaped pet squirrel was spotted in to watch it.
In the later half of the 19th century, there was a popular movement in park design and management in the US that said that making city parks more natural was essential to the health and wellbeing of city dwellers who did not have time to get out of the city. As part of that many cities purposefully released squirrels into their parks.
This is also why you find Eastern gray squirrels in many cities far outside the Eastern gray's native range (which is as you can guess from the name the eastern US). When people wanted to introduce squirrels into, say, Seattle parks they didn't do what you might expect and send someone out to the nearest forest to rustle up some Western gray squirrels to move to the city. No, they had Eastern grays shipped across country and released those in Seattle parks.
The reason for this is that in many areas the native trees are not the kind of trees people like in their parks and so city parks often were largely populated by imported trees from the eastern US. If those imported trees did not produce the kinds of nuts and seeds that the native squirrels like, then native squirrels weren't going to work out in the parks so they brought in squirrels from where the trees came from.
Unfortunately, Eastern grays aren't very picky eaters. They are quite happy eating the nuts and seeds from the native trees and so quickly spread from the parks to the wild and have largely replaced the native Western gray squirrels in Washington. I think the Western grays here are down to just one population.
(The other native squirrels here, Douglas, Red, and Northern flying) weren't affected much by the spread of Eastern grays because they fill sufficiently difference niches in the ecosystem. With Western grays on the other hand Eastern grays are essentially slightly smaller versions of them that like a much bigger variety of nuts and seeds).