The timeline for the establishment of the City and the Capitol Building is -
July 16th 1790 - Congress, meeting in New York, passes the Residence Act - which moves the seat of government to Philadelphia for 10 years, and then to a new site (a square of 10 miles on each side) on the Potomac - the exact area to be established by the President.
Washington selected an area which included the existing settlements of Georgetown and Alexandria - but the new city was on the Maryland side to the south and east of Georgetown. L'Enfant prepared a map showing the outline of the new city and its major streets and buildings in 1791.
1791 First public sale of lots within the Federal District
1792 Competitions were announced for the design of an Executive Mansion (now the White House) and a building for the Congress. The Executive Mansion was sorted out with ease, but none of the plans for the Congress Hall satisfied the Commissioners. William Thornton requested and was given permission to submit a late entry. This design was chosen. However his only professional competitor - Stephen Hallet - was, in compensation for the work he had done on his own entry, given a key role in building - and he abused his position to alter and undermine Thornton's plan. He was eventually discharged.
Sept 18th 1793 - the Cornerstone of the Capitol was laid
late May 1800 - The government left Philadelphia - to set up in Washington
Nov 17th 1800 - The North (Senate) Wing of the Capitol was ready - but the House Building was barely more than foundations. So both Houses met in the Senate Building. A temporary House of representatives building was available by December 1801.
1811 - the House Building was completed - but the middle building remained unbuilt - so the two Houses were joined by a temporary passageway.
Aug 24th 1814 - the British burned the Capitol Building!