Or before.
This is my first comment in this subreddit so hopefully I meet the criteria...
America's independence was official with the signing of the Treaty of Paris. America needed a governing body to sign than treat though since technically the 13 colonies where individual nations that came together for a war. So these 13 colonies formed a confederation called the Articles of Confederation.
Now the Articles of Confederation was a weak governing body that really had no power at all since the states (colonies) kept the power for themselves. This body is going to be a massive failure but was the government of the America post Revolutionary War.
On to your question, during the Articles of Confederation there were 16 presidents voted in. These 16 served over a 14 yr period with the longest serving for a year and a half. The position of President was not a prestigious one like it is today. Thankfully the founding fathers met for the Annapolis Convention to decide trade disputes but the greatest accomplishment of this convention was to set up another Convention after to resolve the weaknesses of the Articles of Confederation (the current government). The second convention is going to be called the constitutional convention which is where....you guessed it, the Constitution is drawn up.
Our founding fathers wanted a leader like a president, but did not want that person to have any chance at a tyranny. They discussed making him a king but eventually decided to divide the powers to three branches (Legislative, Executive (president), and Judicial).
So yes, a president was desired because there needs to be a leader the nation can look too. But they didn't want him to have total power so they put checks and balances in place. Hope this answers your question:)