The Second Continental Congress drafted and approved the Declaration of Independence in 1776. The body was composed of elected officials from each of the 13 colonies to represent that colony. George Washington was not elected to this congress.

We have a very strict republican tradition in America, where those who are voted are the ones who cast the votes, if that makes sense. A deep respect for the rule of law and power sharing has made each transition of power incredibly smooth compared to many other emerging democracies. There are rules we all play by and we do so in a very gentlemanly manner. So in the case of the Second Continental Congress, no one was going to invite George Washington (unelected) to come sign the document, as that would carry no legal weight.