Who first started colonizing?

The answer is lost in obscure early history, probably long before writing existed.

Every major group, tribe, or nation of people has almost certainly expanded its territorial boundaries at the expense of smaller, weaker neighbors. Sometimes these smaller groups were absorbed, sometimes expelled, and in many other cases reduced to a subservient status or caste. The largest groups of Asian peoples, like the Chinese, the ancient Indian Aryans, etc., expanded over weaker peoples, as did powerful Western Hemispheric groups like the Aztec, the Incas, and others. Ethnolinguistic patterns show an arc of conquest in Africa that happened many centuries ago, extending from north to south. The European process of colonization is very clearly recorded from well before the time of Alexander and the Greeks. The Romans established settler colonies all over Europe, including Britain.

About 500 years ago Europe's technical ascendancy in certain fields, like ship construction, allowed some Europeans, most notably the Dutch, Portuguese, Spanish, English, and French, to establish both settler colonies and colonies of occupation overseas, in the Americas, Asia, and Africa.

Though greatly reduced in scope, elements of the colonization process continue in the 21st Century. Examples include Israel in the Palestinian West bank, and the Han Chinese in Tibet. United Nations resolutions and laws which forbid the acquisition of land and political annexation through military conquest compel nations like China and Israel to make various claims to the territories they seize, but these places are colonized nevertheless.