What established US as a formal world empire was Truman's response to the Korean War. The US said "we are going to provide security for other countries against the communists." Then North Korean invaded the South and the communists told the US to put its money where its mouth was. So, we did. Had we shrugged and went back to pre-WWII isolationism, history would have gone very differently.
Truman was responsible for all the post-WWII fallout which made the US a global superpower, not FDR.
What established the US as a "formal world empire" was, in chronological order:
The creation of the Bretton Woods system (1944)
The occupation of Japan and Germany (1945)
The creation of the United Nations (1945)
The establishment of the Trust Territory of the Pacific Islands (1947)
The proclamation of the Truman Doctrine (1947)
The Berlin airlift (1948-1949)
The decision to make the giving of money and weapons to Greece and Turkey public policy whereas before it had been kept semi-secret (1948 )
The formation of NATO (1949)
The Korean War answered the question of whether the United States would intervene directly with its military against communism outside of Europe, it did not establish the US as the center of the anti-communist world. That had already happened
This thread simplifies history, omits history, mixes up history, and gets history plain wrong again and again and it's pretty funny