The Irish, Germans, & Swedish push back the frontier, while the eventually established New York. who's established new york?

Dutch

Explanation:

Before the city's called new York, it was previously called New Amsterdam. It's a city that controlled by the Dutch India company for their interest in north America. New Amsterdam was led by Dutch Governor Peter Stuyvesant. But he was considered to be a bad leader, among the settlers.

So, a coalition between natives Americans and the Europeans supported by the British empire took over the city and named it New York. Because of this, We can say that New York was actually established by the Dutch even though it's currently named after a region in England.

Some of them were just simply good people.