George Washington took the oath of office on 30 April 1789. At that time he was officially the President of the United States.
John Adams was inaugurated as the Vice President on 21 April 1789.
According to the US Constitution (Article 2 Clause 6), if the president is unable to discharge the powers and duties of the office, the vice president shall act as president.
When John Adams became the vice president, George Washington had not yet taken the oath of office. This means Washington was not able to act as the president, until 9 days after Adams took office.
George Washington was officially the first elected president of the United States. However, John Adams was the first person with the ability to act as the president.