No, the capital city of the United States was not always Washington, D.C.
Initially, New York City served as the first capital under the U.S. Constitution. It became the capital on September 13, 1788, following its role as the de facto capital since 1785. During this period, New York City hosted the nation's legislature and housed the capital building, Federal Hall.
However, after considerable debate, it was decided that New York City would not serve as the permanent capital. In 1790, Congress voted to relocate the capital to Philadelphia, citing various concerns including the commercial nature of New York and fears of aristocratic influences. Philadelphia served as the capital until 1800.
Washington, D.C. became the capital of the United States later, in 1800, when the federal government officially moved there. The city was chosen as the permanent capital to provide a neutral ground between the northern and southern states and to symbolize a fresh start for the nation's government.