On September 1, 2021, González was promoted to the major leagues.[5] He made his MLB debut on September 3 as a pinch hitter, going 0-for-2 against the Kansas City Royals.[6] On September 8, he got his first hit, a pinch-hit single off Oakland Athletics pitcher Andrew Chafin.[7] He finished his rookie campaign playing in 10 games and going 8–for–32 (.250) with 2 RBI.
On September 3, 2022, González hit his first career home run, a three–run shot off of Minnesota Twins starter Aaron Sanchez.[8]
González hit .194 in 44 games for Chicago in 2023 before he was placed on the injured list with right shoulder inflammation on June 19, 2023.[9] He was transferred to the 60-day injured list on July 2.[10] On August 11, it was announced that González had undergone surgery to repair a labrum tear in his shoulder and would miss the remainder of the season.[11] González was designated for assignment by the White Sox on January 26, 2024.[12]
Boston Red Sox
On January 31, 2024, González was claimed off waivers by the Boston Red Sox.[13] He was optioned to the Triple–A Worcester Red Sox to begin the 2024 season.[14] González was recalled to Boston on April 9,[15] then placed on the injured list four days later due to a left wrist sprain.[16] He remained on the injured list until being activated on May 8.[17]