Warning: SPOILERS for Star Trek: Discovery Season 3 Finale - "That Hope Is You, Part 2"
Michael Burnham (Sonequa Martin-Green) became a Captain in Star Trek: Discovery season 3, and she is simultaneously one of the youngest and also, along with Saru (Doug Jones), one of the two oldest Captains in the 32nd century Starfleet. In fact, considering her tumultuous and eventful Starfleet career and the number of times she's saved the galaxy, Michael is still remarkably young. Yet Captain Burnham still isn't the youngest Captain of a Star Trek series.
Michael is the primary protagonist of Star Trek: Discovery and she was introduced as a rising star in Starfleet in season 1. In 2256, Commander Burnham was the First Officer of the U.S.S. Shenzhou, having served with and was mentored by Captain Philippa Georgiou (Michelle Yeoh) for seven years. However, Burnham blew up her career by igniting a war with the Klingons, albeit she was misguidedly trying to prevent that same war, which resulted in Georgiou's death and the destruction of the Shenzou. Michael was stripped of her rank and imprisoned as Starfleet's first mutineer. However, Burnham found herself transferred to serve aboard the U.S.S. Discovery as an unranked Specialist and she courageously redeemed herself and ended the Klingon War. Burnham was reinstated as a Commander at the conclusion of Star Trek: Discovery season 1. Michael Burnham was born in 2226, so she was 30 when she was imprisoned and Michael was 31 in 2257 when the Klingon War was over.
Star Trek: Discovery season 2 picked up immediately after season 1 and its events spanned the course of the next year. The U.S.S. Enterprise's Captain Christopher Pike (Anson Mount) took command of Discovery and their mission was to investigate the red signals in space. This ultimately revealed a plot by Control, Section 31's artificially intelligent threat assessment system, to wipe out all organic life in the galaxy. Discovery's acquisition of Sphere Data, which contained 100,000 years of galactic knowledge, was crucial for Control to achieve its goals, and the only solution was for Commander Burnham to become the time-traveling Red Angel and lead Discovery and the Sphere Data into the distant future to keep it from Control. When Michael and Discovery permanently left the 23rd century in 2258 at the conclusion of Star Trek: Discovery season 2, Commander Burnham was 32.
In Star Trek: Discovery season 3, Burnham arrived in the year 3188 but she landed alone, although she was elated that her plan worked and she "saved all the things". After Michael destroyed the Red Angel time suit, Michael realized she was stranded in the 32nd century. Luckily, she made a friend, Cleveland Booker (David Ajala), who would become her love interest, and who told her about The Burn that altered the fate of the galaxy. Uncertain if her friends aboard the U.S.S. Discovery would ever join her in the future, Michael became a courier like Book and spent the next year investigating what caused The Burn. Finally, after a year, Discovery arrived in the 32nd century and reunited with Burnham, who declined the Captain's chair so that Saru could deservedly become Captain. By then, it was 3189 and Michael was 33 (or 963 chronologically).
While the defined chronology of Star Trek: Discovery season 3's events is unclear, fans know that timeframe included a three-week retrofit of the U.S.S. Discovery-A after they arrived at Federation Headquarters. Fans also know that there was another time jump at the end of Star Trek: Discovery season 3's finale after Burnham killed Osyraa (Janet Kidder), defeated the Emerald Chain, and saved the Federation. Therefore, while most of Star Trek: Discovery season 3 occurred in 3189, it's possible that the calendar turned a page and it is now 3190 by the time Michael accepted a promotion and took command of the Discovery, which would likely make her 34 (or 934) by the time she became Captain Burnham.
This makes Michael Burnham amazingly young to be a Captain, although she has far more experience than most Starfleet Officers her age. However, Burnham still doesn't match Captain James T. Kirk. The Prime Universe's version of Kirk played by William Shatner was 32 when he became Captain of the Enterprise. And, incredibly, the Kelvin timeline's version of Kirk played by Chris Pine became the Enterprise's Captain at only 25! But Burnham was originally expected to become a Captain before her mutiny and, as Admiral Vance (Oded Fehr) reminded Burnham, after 930 years, she "waited long enough" for Star Trek: Discovery's big chair. Indeed, no one, not even Saru, waited longer to become Captain than Michael Burnham.