The U.S. defeat of Spanish forces in Cuba in 1898 dealt a decisive blow to the already declining Spanish imperialism and the resulting U.S. occupation of another former Spanish colony, the Philippines, gave the United States the solid East Asian foothold it had long been seeking. Although the global reach was thereby extended, the idea of Superpower status is associated with a later era, post World War II, and the Cold War contests with the Soviet Union.
The struggle for women suffrage had heated up in the mid-19th century as the women's movement built on the Seneca Falls Convention's success. The Civil War and the Reconstruction's attention to African American emancipation, rights, and male suffrage pushed women suffrage to the back burner.
The period in which U.S. international expansion and military power are associated most closely with women suffrage is the World War I era and its aftermath. Even as women played significant roles in the war, especially as nurses, the suffragists ramped up their efforts. In 1917, the year the United States entered the war, Alice Paul and associates marched in Washington, chained themselves to the White House fence, and went on hunger strikes.
President Wilson had opposed women suffrage as a distraction from the war and, like his fellow Southerners, worried about the effect of black women voters. After the war, noting women's contributions--influenced as well by England recognizing women suffrage in 1918, barely a week after Armistice--Wilson finally backed it in the United States, by the Constitutional Amendment that was already moving ahead.
With the last state's ratification (Tennessee), the 19th Amendment became part of the Constitution in August 1920.