Colonialism didn’t begin with international trade, because the colonies were part of the colonising nation.

That's imperialism.

It's possible to establish colonies without having a motherland controlling them. Consider the original settlement of Polynesia, or the establishment of new cities by the Sea Peoples. And even when there's a motherland, it's possible that colonies will still compete with each other: for example, the Moorish kingdoms in Spain, which had roots in different ethnicities and tribes in Morocco and fought with each other like crabs in a bucket, which was why the relatively backwards Catholic Monarchs were able to eventually drive them out.

It's also possible to have empires without colonization-- subverting local rulers, then pulling their strings. Much US imperialism has been like that: there's interference in Central and South America, but the US didn't replace the local elites with Yanks. They just bought them off and helped them send their kids to Harvard and Yale.