Let’s start with the beginning.
Before the building that houses those nine robes today was built, we had the Merchants Exchange Building in New York City and Old City Hall in Philadelphia as the ‘seat’ of the court. (Though there’s the circuit riding Jay and co. had to do for a while, but I’m jumping ahead.)
West v. Barnes was the first case heard by the Supreme Court. It’s heard on August 2nd. Mozart is to die at the beginning of December. The Bill of Rights has yet to be ratified.
John Jay’s appointment to Chief Justice served -- in the words of Walter Stahr -- as a way to evenly split Hamilton and Jefferson. With Jay on the bench, Jefferson had somewhere appropriately senior to go (the State Department) and Hamilton could head to the Treasury.
Quoting Stahr --
The Supreme Court met for the first time on February 1, 1790, in the Exchange Building in New York City. The ground floor of this brick was an open public market, cleared for the day to keep down the noise, and the upper floor a courtroom, ‘uncommonly crowded’ that day with state judges, members of the bar and others.
The first case they heard -- though it should be reemphasized that the above-quoted scene was merely the first day they met, not the day of the first case (two Justices couldn’t get there in time, so a group -- including the Justices -- toasted the eventual evening away after the day’s session had come to an end) -- concerned an attempt to evict a landowner from his farm.
The man bringing the suit was claiming William West couldn’t pay off his mortgage using paper currency. David Barnes wanted silver or gold. The Court dismissed the case because the appeal that brought Barnes before the Supreme Court had been issued from a Rhode Island Court, not the Supreme Court itself. This set in motion what would eventually become the Judicial Act of 1792.
Meanwhile -- Jay quipped he could find his way across the country by the light of his likeness burning in effigy. (The Jay Treaty wasn’t a popular treaty.)
The other justices at the time included James Wilson, William Cushing, John Blair Jr, and John Rutledge.