One common element is the presence of a heroic figure. For example, in the founding myth of Rome, Romulus is seen as a heroic founder. Another element can be a divine intervention. Many origin stories involve gods or supernatural beings guiding the creation of a nation or community. Also, a significant event like a great battle or a natural disaster often plays a role in shaping the founding myth origin story.
Well, often there is a sense of purpose in founding myth origin stories. They are meant to give a sense of identity to a group. In the case of the founding of the United States, the idea of freedom and a new start was a big part of the origin story. Additionally, there might be a struggle against an enemy or a difficult situation. This struggle then becomes part of the narrative that unites the people who identify with the founding myth.