Tucson with an 8–7 record and a 3.75 ERA in 20 games. He was selected to participate in the All-Star Futures Game on July 13 in Chicago, working a scoreless frame for the World Team. González was promoted on June 1, 2003, to face the San Diego Padres at Qualcomm Stadium. Arizona won the game 10–4. He picked up his first major league win, pitching 5.2 innings allowing 10 hits for 3 runs and striking out 4. He also collected his first major league hit. He had another start on June 6 against the Indians at Arizona where he took his first loss before returning to Tucson. When the rosters expanded in September, he was called up and pitched in 7 games (all in relief). He finished the season with a 2–1 record and a 4.91 ERA. González had a rough year in the major leagues in , mostly because pitching with a torn fingernail for most of the year ended his season short. In several stints with the big club, he ended with 0–9 record with a 9.32 ERA in 10 starts for the Diamondbacks. His best game came August 29 in Cincinnati where he took a no-hitter to the 7th inning and lost it to an infield hit by Felipe López and later lost the shutout to a home run by Adam Dunn. was the redemption year for González. After a rough 2004 in MLB and spending almost the complete 2005 season in the minors, Edgar stated his case for a spot in the rotation for the next year. He was called up in June to replace in the rotation Russ Ortiz who was released. He pitched two good games (quality starts), but lost the two because of no run support. After Juan Cruz was activated from the disabled list, González was moved to the bullpen where he struggled to adapt and was demoted to Tucson on July 19 to continue to pitch as a starter. He returned to team on September and took the place in the rotation of struggling Enrique González. He had 3 starts in September, the 3 being excellent games, reaching 7 innings in two of them and not allowing more than 2 runs in each game. He ended the year 3–4 with an ERA of 4.22. His record as a starter was 2–3 with a 3.00 ERA. was the first year González started