New York City was the first capital of the United States under the Constitution, before Philadelphia and Washington, D.C.
The First Congress met at Federal Hall in New York City in 1789. George Washington was inaugurated there on April 30, 1789, making the city the first national capital under the new constitutional government. The ceremony marked the beginning of the executive branch’s operations.
Congress passed the Residence Act in 1790, choosing a future permanent capital on the Potomac River. Philadelphia then served as the temporary national capital from 1790 to 1800. Washington, D.C., became the permanent capital in 1800.
This answer requires a precise definition of “first capital.” During the Revolutionary War and the Confederation period, Congress met in several cities, including Philadelphia, Baltimore, Annapolis, and Princeton. Those earlier meeting places belong to a different constitutional era, so they are not the first capital under the Constitution.