The first Cy Young award wasn't presented until 1956, and even then there was only one awarded for both leagues. Here I argue who should have been the lone winner, and pick who should (would?) have won in the other league as well:
1956 Don Newcombe over Herb Score
In an MVP-winning performance, Newcombe also took home baseball's first-ever Cy Young award on the strength of his 27-7 record, which gave him the most wins and best winning percentage in baseball. But the real Cy Young pitched in the American League, and didn't even make the ballot. Young Herb Score, just 23 and coming off his sensational rookie campaign, led all of baseball in strikeouts, adjusted ERA, H/9 and K/9. Score also led the league in shutouts and ranked second in wins (20), winning percentage, raw ERA (2.53, more than half a run better than Newk's 3.06), and pitching WAR with 7.3. He pitched nearly 250 innings, almost as many as Newcombe's 268, so there's really no viable argument for Newcombe over Score. Unfortunately, Score was struck by a line drive off the bat of Gil McDougald the following spring and was never the same.
1957 Warren Spahn--no argument
1958 Bob Turley over everyone else
Turley wasn't even the best pitcher on his own team, let alone all of baseball. Rotationmate Whitey Ford was the major league ERA champion with his microscopic 2.01 mark, which translated to baseball's best ERA+ (177) as well. He also led the majors in shutouts (7) and WHIP (1.08), but somehow failed to even crack the ballot. He was probably hurt by the fact that Casey Stengel only started him 29 times, which limited Slick to "just" 219.1 innings. Warren Spahn, Lew Burdette, and Bob Friend, the three men who finished behind Turley, all threw at least 274. Even so, bWAR rates Ford more valuable than all of them.
1959 Early Wynn over Sam Jones
Wynn won an ML-best 22 games and pitched the most innings in the American League (255.2) with a 3.17 ERA, but somehow that wasn't even worth three wins above replacement. Teammate Bob Shaw, who pitched 25 fewer innings but did so with a 2.69 ERA, was worth nearly five bWAR but finished third, even though he had a better case. Not as good as San Francisco's Sam Jones, the runner-up, who led the Senior Circuit with 21 wins, a 2.83 ERA and four shutouts. He also threw 270.2 innings, fourth most in baseball, and struck out 209 batters, second only to Don Drysdale.