No Japan was under what was essentially military occupation for about 6 years after the end of the war in August 1945.

Soon after over a quarter million mostly US troops were landed around the Home Islands, to serve as an occupation force, along with aiding in rebuilding the thoroughly devastated nation, and stabilize a bombed out economy with rampant food distribution problems.

While Japan retained a skeleton govt, including Emperor Hirohito, and a Diet, the true power was with the US authorities. The occupation was organized under the General Headquarters of the Supreme Commander of the Allied Powers. Namely through General Douglas MacArthur. His office and subordinates were tasked with rebuilding Japan into something of a Western liberal Democracy, and they set out to do just that, including writing the first drafts of the new post war constitution for Japan.

However bit by bit the US presence was reduced, and with the start of the Korean War and Communist victory in the Chinese Civil War, US focus was drawn elsewhere and the occupation of a Japan on its way to rebounding was becoming redundant. Thus in 1951 the Treaty of San Francisco was signed to settle most outstanding matters from the end of the war. Among other things this returned sovereignty to Japan and their domestic govt from the occupation force.

So while Japan was run by the US essentially for several years, they were not in any sense part of the US because of it.