Daza signed with the Colorado Rockies as an international free agent in October 2010. He spent his first three professional seasons (2011-2013) playing for the Rookie-levelDSL Rockies. He played for the Rookie-levelGrand Junction Rockies in 2014, hitting .370/.415/.490/.905 with 4 home runs and 35 RBI. He split 2015 between the Low-ABoise Hawks and the Single-AAsheville Tourists, accumulating a .325/.358/.451/.809 batting line with 3 home runs and 53 RBI. He split his 2016 season between Asheville and the High–AModesto Nuts, hitting a combined .303/.338/.402./740 with 3 home runs and 61 RBI. He spent 2017 with the High–ALancaster JetHawks, hitting .341/.376/.466/.842 with 3 home runs and 87 RBI.[1] Daza played for the Salt River Rafters of the Arizona Fall League after the 2017 regular season.[2]
The Rockies added him to their 40-man roster after the 2017 season.[3] He spent the 2018 season with the Double-AHartford Yard Goats, hitting .306/.330/.461/.791 with 4 home runs and 29 RBI. He appeared in just 54 games in 2018 after suffering a left shoulder injury in late July of that season.[4] Daza opened the 2019 season with the Triple-AAlbuquerque Isotopes.[1]
The Rockies promoted Daza to the major leagues for the first time on April 9, 2019, when David Dahl was placed on the injured list.[5] Daza made his major league debut on the same day, versus the Atlanta Braves.[6] Daza did not appear in a game for the Rockies in 2020, despite injuries to David Dahl and Ian Desmond's decision to opt out of the season due to the COVID-19 pandemic.[7] For the majority of the 2021 season, Daza was the starting center fielder for Colorado up until his injury in August. He ended up hitting .282 with 2 home runs and 30 RBI in 107 games.
Daza played in 113 games for the Rockies in 2022, slashing .301/.349/.384 with 2 home runs and 34 RBI. In 24 games to begin the 2023 season, he batted .270/.304/.351 with no home runs and 7 RBI. On May 5, 2023, Daza was designated for assignment following the waiver claim of Austin Wynns.[8] He cleared waivers and was sent outright to Triple-A Albuquerque on May 8.[9] In 39 games for the Isotopes, Daza batted .305/.350/.415 with 2 home runs, 19 RBI, and 4 stolen bases. He elected free agency following the season on November 6.[10]