This is a great question. A little history would help here.
First, the 20th century was destructive for many powerful nations on account of wars. For example, Europe was ravaged by warfare as well as the Soviet Union. There was much infrastructural damage and the need to rebuild after World War I and II. The United States did not have to deal with this, because the war was fought in Europe and not in North America. This fact alone put the United States ahead.
Second, the rest of the world - Asia and Africa were still weak. So, they could not really challenge America. Hence, we can say by default America became a super power.
Third, as the economy grew after the war, America continued to climb in power, wealth, and prestige. In light of this, soon America became a super power.