Kind of a tough question due to the way its formulated.

through the 19th century, the great powers of europe had an average amount of +-300.000 men under arms. (Paul Kennedy's "The Rise and Fall of Empires). The USA had about 25.000 on average. At the same time, the USA had a significantly higher population then any-but-Russa, but was lacking in the industrial capacity and necessity to maintain a large standing army. During the First World War the USA fought as a "Major power", side by side to the french and especially british empires.
Whilst during/in the aftermath of the Second World War, they were, together with the USSR, "World powers".
In the 1990's the USSR was dissolved, leaving the USA as THE "World power".

So depending on the content of the question, these are the dates id give as the points they were considered a great power? By 1916 they were to be counted on as one of the powerfull players on the global sphere, but were focussed on isolation. By 1946 they were arguably the most powerfull country on earth and started to extert a lot of political and economical pressure.
By 1992 no single nation or organisation could challenge them on political, economical or military superiority.

Personally i would pick 1946 as the "Fixed point" where the USA became a world power, as every other country on earth was either in shambles or did not have enough industrial power to challenge them. And since then, nobody caught up with the quickly growing American economy.

PS: (Im more of a history geek then a historian, but i figured id give it a shot as nobody answered)