Well, an earlier Presidency is plausible, but not by much. In my "Washington Wins At Brandywine" TL, I posit the Br5itish having a lackluster year in 1778 after 2 successive major defeats in '77 (that and Saratoga) and suing for peace, which comes in 1779. The Articles of Confederation aren't totally agreed to when further problems happen, and so John Adams - fresh off working the Massachusetts Constitution, which is similar to OTL U.S. one, helping to push for a Convention in 1781. The result is Washington being President 6 years early.
Now, Franklin was in his late 70s at that point, aged but probably capable of one term since he was at the 1787 Convention OTL. Let's suppose that there is backlash against Adams and the President is seen as more of a figurehead. Franklin could then win in 1783 and promise4 to serve only one term, with the understandign that he doesn't have a lot to do; the Executive branch is so small there isn't even a VP.
Then, we could still get a stronger Executive akin to OTL - just have something like Shay's Rebellion or the Whiskey Rebellion take place and Franklin himself calling for it. As Washington leads troops against them in 1785 or 1786, people call for him to be a stronger President, and he then declines as per OTL unless he is not givent he huge amount6 of power that some want him to have. So, it becomes close to OTL.
(In my TL, BTW, I had Washington appoint Franklin Postmaster General in 1783 to give him a post int he first Cabinet, if only for a year or two.)