What, according to the Declaration, makes the American colonists a distinct "people," entitled to a "separate and equal station" among the people of the world?

The Declaration of Independence states that it is the laws of nature and the God that created those laws which determine the separate and equal station of a people. What the Declaration is trying to establish here is the idea that there is a higher law that has been violated by the British in their high-handed treatment of the American colonists. In this reading, the principle of national self-determination is natural, not artificial; it is one of the natural, inalienable rights with which God has endowed humankind.
As with elsewhere in the Declaration, we can observe here the influence of the Enlightenment, which insisted that human beings enjoyed a number of rights simply by virtue of being human. And one of these rights is the right to join with other like-minded individuals to form an independent nation, free from the control of a colonial power.
https://www.archives.gov/founding-docs/declaration-transcript