Speaking just as an American who has studied American history, the situation there happened first gradually and then suddenly.
The biggest thing to understand is what settler colonialism is, though. It’s not even like living in a smaller city in a European country and still thinking about yourself as a member of that culture.
It’s being far away from the source of your culture, separated by (in these cases) ocean, over a significant period of time. In the American case, as long as 169 years. Being a colonial settler is a particular experience. You are a legal/political part of a nation/culture you have never directly seen, in most cases. Depending on when your ancestors left the mother country, you could have grandparents or great-grandparents who never saw it. You are surrounded by different nature: animals and plants your mother language needed to adopt new words for. You are surrounded by the indigenous people of the continent you live on, and you have complicated relationships with them. The new little societies your direct settler ancestors built do not have the aristocracy or the religious institutions of the origin culture. Maybe your religious group is not common in the mother country.
This is all happening, in the American case, before even the telegraph was invented, so you really only learn about the home culture through books and products that you trade for. (One reason that the famous event during the American Revolution, the destruction of the tea in Boston, was so meaningful to the colonists was because tea-drinking was and is this marker of Britishness.)
But you fight in wars for that mother country, so it can build the empire you are part of. You help win those wars, and after the <em>fourth one </em>against your mother country’s great rival, that country loses its own empire on your continent. You are joyful! You feel so proud to be a part of your mother culture! But your mother country wants more control now...