After signing, May made his professional debut with the Arizona League Dodgers, and spent the whole season there, posting an 0-1 record with a 3.86 ERA and 34 strikeouts in 302⁄3 innings pitched.

[3] In 2017, he played for both the Great Lakes Loons and the Rancho Cucamonga Quakes, compiling a combined 9-6 record, 3.63 ERA, and a 1.15 WHIP in 25 games (24 starts) between the two clubs.

[11] On August 13, May picked up his first big league win against the Miami Marlins after pitching 52⁄3 innings, allowing one run on three hits with five strikeouts.

[13] May was selected to start for the Dodgers on Opening Day in the pandemic-shortened 2020 season after Clayton Kershaw injured his back before the game.

[17] On August 20, 2022, May made his first start after returning from his recovery and struck out nine while allowing only one hit in five scoreless innings against the Miami Marlins.

[18] He pitched a total of six games for the Dodgers, with a 2–3 record and 4.50 ERA[13] before he was placed on the injured list with lower back tightness on September 24, ending his regular season.

[24] On July 4, it was announced that May would undergo surgery on the flexor tendon in his right elbow, as well as a Tommy John revision for a Grade 2 UCL sprain.

[13] May and the Dodgers agreed to a $2.135 million contract for 2024 in salary arbitration[26] though he began the season on the 60-day injured list as he continued to recover from his surgery the previous year.

[29] A tall pitcher at 6 ft 6 in (1.98 m), 180 lb (82 kg), May pitches with a three-quarter stance with high leg lifts both before release, and at follow-through (with nobody on base).