By the time George Washington was elected as President, he already had much experience as a leader and with Congress. As a matter of fact, Congress created the idea of the president of the United States because of George Washington. First, Washington fought during the French and Indian War, but he did more than that.
He led troops during this war which helped make his name known as a military leader for the Virginia Militia. Then he was appointed as the commander in chief of the Continental Army and led them to victory during the American Revolutionary War.
From this, many men in Congress felt long before the presidency that George Washington was the man for the job. He wanted a national Constitution.