"establishment of the first" is correct and usable in written English.
You can use it to refer to the first instance of something being created or established. For example, you could say, "The establishment of the first American colony was an important moment in history."
The establishment of the first Muslim centres in Indonesia was probably a result of commercial circumstances.
Fought between the Minamoto and Taira clans in the 12th century, they resulted in the establishment of the first shogunate.
She carried a major responsibility for the establishment of the first child abuse registry in the City.
He pioneered the establishment of the first Middle College High School in the United States, at La Guardia Community College, and later the International High School in Queens.
They also remember that President Woodrow Wilson played a major role in the establishment of the first Czechoslovak state in October 1918.
Respect for the individual, Shorto claims, was behind Amsterdam's tolerant religious policies, its establishment of the first stock market, and, with Rembrandt, its development of secular art.
Since the establishment of the first studios, a century ago, there have been few movie executives as dominant, or as domineering, as Harvey Weinstein.
His minister of education, Victor Duruy, carried out an enlightened program of broadened public education, including the establishment of the first secondary education for girls.
The area's growth began with the establishment of the first cotton mill in the southern United States, at Graniteville in 1845.
His speech led to the dissemination of nuclear technology for civilian purposes and the establishment of the first nuclear power stations.
Governor Rockefeller's establishment of the "first state arts council in the nation, a prototype for the National Endowment of the Arts" — the New York State Council on the Arts — stands out for me.
