Earlier quoted context omitted.
You only missed the part that SpaceX was founded several years prior and that Falcon 1 was developed with his own money and solely private risk. Nasa only contracted SpaceX because of that AND because SpaceX saves them billions of dollars from otherwise inefficient suppliers. But that's not relevant.
You must have read Elon's own tales. See who Michael D. Griffin is and his history with Elon.
https://www.sec.gov/edgar/browse/?CIK=1181412
Musk & Griffin had a relationship around establishing a Mars colony even before SpaceX foundation. Musk even tried to recruit Griffin when assembling SpaceX founding team.
Book: Liftoff, p. 11 - https://books.google.com.br/books?id=DQ7jDwAAQBAJ&printsec=f...
By 2005, SpaceX was already leasing a launch pad for Falcon 1 and Falcon 5.
https://spaceflightnow.com/falcon/050120lc36/
In 2006, Nasa contracted SpaceX, referred by Griffin in the link you shared.
https://www.nasa.gov/wp-content/uploads/2015/04/189228main_s...