What led the united states to build its military forces after winning a successful war?

The United States built up its military forces after the end of World War II because of the threat posed by the Soviet Union. Immediately after the war, the Soviet Union erected puppet governments in Romania and Poland. It was at this time that Stalin uttered his famous pronouncement:

The war against fascism has ended; the war against capitalism has begun.

The U. S. withdrew troops from Eastern Germany, which was largely occupied by the Soviets, and had hoped the Soviets would do the same. They refused, and began arresting and punishing those who spoke against the puppet government which they soon erected in East Berlin.

In 1946, Stalin had stated that peace was impossible

under the present capitalist development of the world economy,

The U. S. and other western powers then were convinced that the Soviets intended world domination, including the destruction of western society and democracies. When Secretary of State James F. Byrnes threatened to use nuclear weapons in an attempt to force the Soviets to back down, he was ignored.

It then appeared that the U. S. would need to be prepared to face the Soviet threat head on. The policy was best expressed by a former ambassador to the Soviets, George F. Keenan who stated that the Soviets would

attempt to fill every nook and cranny available at the basin of world power.

Keenan said that the response of the U. S. should be:

A long term, patient but firm and vigilant containment of Russian expansive tendencies ... Such a policy has nothing to do with outward histrionics: with threats or blustering or superfluous gestures of outward toughness.

From his remarks was born the policy of containment which necessarily entailed the buildup of the U. S. military.