When the ninth state, New Hampshire, ratified the Constitution in the summer of 1788, the tenth Confederation Congress set the dates for the new government to start: On January 7, 1789, states would choose electors; on February 4, the electors would cast their ballots for president; and on March 4, the new legislature would meet to begin business, the first order of which would be to count the votes and arrange to have the president -- Washington, everyone knew that -- sworn in.
Things didn't quite work out according to that timetable, however. Bad weather delayed many members of the First Congress in their journeys to New York City, the temporary capital, and it wasn't until April 6 that a quorum could count the votes and transmit a message to Washington that he'd been elected. He acknowledged it and came as soon as he could -- toward the end of April. All the arrangements were made, and the first inauguration was April 30, 1789.
But it was to be March 4 after that, the Second Congress decided, and apparently Washington had no objections, so his second term began on March 4, 1793 after his unanimous re-election. All together there were 32 inaugurations on March 4 in U.S. history. (The picture is from one such day, March 4, 1913, as Taft left office and Wilson became president.)