Braxton's first encounter with the U.S.S. Voyager (relative to Voyager's perspective) took place when he travelled to the year 2373 in the Delta Quadrant to destroy the Federation starship. In his experience, Voyager was associated with a temporal explosion that would obliterate Earth's solar system in the 29th century. In confronting Voyager, Braxton's ship was thrown back in time, where it crash-landed on Earth in 1967. Braxton survived the crash, but became separated from his ship. Stranded in the past, Braxton watched helplessly while a native of the period, Henry Starling, salvaged the Aeon and exploited its technology over the next three decades. In 1996, Braxton was homeless and destitute. It was that year that Voyager found itself in Earth orbit. Captain Janeway and crew tracked down the Aeon, which Starling planned to fly into the future, and destroyed it before Starling could make the time jump. This action prevented the 29th-century explosion and created an alternate timeline in which Braxton was not trapped in the 20th century. This Braxton arrived in 1996, in the Aeon, to set things straight and escort Voyager back to the 24th century. Captain Janeway requested that they be returned to the vicinity of Earth, but Braxton cited the Temporal Prime Directive and brought the ship back to the Delta Quadrant.
In a different timeline, Braxton commanded the Relativity in an effort to prevent a saboteur from destroying Voyager with a weapon designed to fracture space-time. Prior to the weapon's detonation in 2375, Braxton recruited Seven of Nine to jump through time to locate where and when the weapon was placed, because her ocular implant was able to detect disruptions in space-time. Eventually it was learned that Braxton himself was the saboteur. An older version of Braxton suffered from temporal psychosis and blamed Voyager for his circumstances — 30 years of exile on 20th-century Earth, the temporal inversion in the Takara Sector, repeated rehabilitation, loss of rank, and forced retirement. The older Braxton was apprehended, and the younger one on the Relativity was arrested by his first officer, Lt. Ducane, for crimes he was "going" to commit. The different versions of Braxton were re-integrated to stand trial, but he was guaranteed leniency in exchange for revealing the precise moment he boarded Voyager to plant the weapon.