It wasn't "a run". He was just one of the random jobbers they used on the weekend shows. They used to use A.J. Styles, Samoa Joe, Chris Daniels, and Low-Ki on the weekend shows a lot as jobbers too during the Invasion era.
I see. Thank you, Wikipedia:
After Danielson graduated from Aberdeen-Weatherwax High School located in Aberdeen, WA in 1999, he decided to pursue wrestling professionally and initially attempted to train at Dean Malenko's wrestling school. Due to its subsequent closure, however, he instead
trained under Shawn Michaels and Rudy Gonzalez at the Texas Wrestling Academy.[24][6] Danielson debuted in Michaels' promotion, the Texas Wrestling Alliance (TWA), and on March 21, 2000, he won his first professional wrestling championship, when he teamed with Spanky to win the TWA Tag Team Championship by defeating Jeromy Sage and Ruben Cruz.
As Danielson continued to tour the country,
he was signed to a developmental deal by the World Wrestling Federation (WWF) to work in their developmental system where recently signed performers train and refine their skills before debuting on WWF's television programming, and was assigned to Memphis Championship Wrestling (MCW). There, Danielson gained exposure, and
was trained by WWF competitor William Regal, who he has credited as being instrumental in the development of his career.[6] It was during this time that Danielson adopted his well-known moniker "American Dragon".[25]
WWF severed its ties with MCW in 2001, releasing Danielson from his contract, but not before he won the MCW Light Heavyweight Championship and the MCW Tag Team Championship with Spanky.[4]
Danielson returned to the company on later dates after it was renamed World Wrestling Entertainment to compete on its secondary programming, Velocity and Heat, initially as enhancement talent before being allowed to compete in longer matches; he once wrestled future WWE Champion John Cena in a losing effort.[26][27]
Danielson also toured Japan with the promotion, Frontier Martial-Arts Wrestling (FMW) with fellow trainee from the Texas Wrestling Academy, Lance Cade, competing in several tag team matches.[1][8] He returned to the country after his release from the WWF, competing in Japan's premier promotion, New Japan Pro Wrestling (NJPW).