This is actually how you start a city though, you build a suburb and wait for it to grow into a city. This takes a really really long time so it's better to build near existing cities.

We don't observe this phenomenon occurring often in the modern day only because cities sprawl rapidly and so the evolution of the suburb becomes a borough of the existing city rather than a brand new city. Otherwise Brooklyn, Jersey City, Weehawken, etc. would all be considered new cities instead of being referred to as the NYC metro.