Of all the Super Saiyans introduced over the course of the Dragon Ball franchise, the character to canonically achieve this powerful transformation at the youngest age is Goten. While preparing for the 25th World Martial Arts Tournament in Dragon Ball Z, Goten shocked his family by revealing himself as the latest Super Saiyan, despite only being seven years old at the time. A popular fan theory indicates that the reason Goten was capable of transforming into a Super Saiyan at such an early age posits that Goku may have been transformed at the time of Goten's conception.
After training with Gohan for a relative year inside the Hyperbolic Time Chamber, Goku determined that he and his eldest son should maintain their Super Saiyan transformations at all times. This strategy minimized the physical strain and power consumption the state had on their bodies, with Goku and Gohan eventually even being able to sleep while transformed. It's during this ten-day period between Goku and Gohan emerging from the Hyperbolic Time Chamber and Goku's heroic sacrifice during the Cell Games that the fan theory, postulated on Reddit by user Logic_Nuke, that Goku and his wife Chi-Chi conceived Goten, with the boy born approximately nine months after the Cell Games and his father's death.
By comparison, the other Super Saiyans to achieve this transformation at similarly young ages came from an immense amount of rigorous training. Trunks, who was eight years old when he first transformed into a Super Saiyan, had trained in his father Vegeta's intense gravity chamber ever since he could walk. Gohan had received several power boosts and trained under Piccolo and Goku before eventually achieving the Super Saiyan transformation in the Hyperbolic Time Chamber at age eleven. By contrast, Goten had only been trained in martial arts by Chi-Chi and only in secret, making his quick transformation all the more striking.
Franchise creator Toriyama Akira explained the science behind the Super Saiyan transformation, including how it was achieved and why it caused users' physical appearance to noticeably change. Toriyama stated that the transformation was facilitated by something he referred to as "S-Cells." Similar to midicholorians in the Star Wars Universe, S-Cells are carried in the blood, and the amount present determines whether a Saiyan can transform, with intense emotions increasing their potential.
With Goku presumably containing a heightened amount of charged S-Cells in his bloodstream when he conceived Goten with Chi-Chi, as he was likely a Super Saiyan at the time, this abnormally high amount of S-Cells was likely passed on to his son to help Goten reach his Super Saiyan state earlier than most of his contemporaries.
Goten is a character that largely fell by the wayside during Dragon Ball Super, but given the age that he achieved what took so many other Saiyans years to reach with intense training, he holds quite an amount of untapped potential just waiting to be displayed. In some ways, Goku knew that he was heading toward his death as he entered the Cell Games, ready to hand over the defense of Earth to his eldest son Gohan and the rest of the Z Fighters. However, in conceiving Goten before his death, he left the world with its youngest Super Saiyan, and one that was on the fast track to becoming one of the planet's most surprising -- and powerful -- defenders.