The Doctor was a Time Lord, and like the Beginner fled from Gallifrey. His TARDIS crashed into the Beginner's TARDIS when he was fleeing, causing his TARDIS to stay in the shape of a police box. (Encounters)
He asks the Beginner to drop him off somewhere before crashing onto a planet. As a result the Beginner and the Doctor become separated on opposing ends of the war - with the Doctor being kidnapped by the Fire Clan General. He formed an alliance with Ice Golem Zarr to escape. Zarr pays him back by killing the Ice Queen who was about to kill the Doctor. They then retreat back to the TARDIS so that the Beginner can hopefully successfully drop the Doctor off like he was supposed to. (When Worlds Collide)
Chronologically in the show, the first encounter of the Beginner and the Doctor was in World War II, however they see to share some history prior to this moment. The Doctor's TARDIS is stuck on a roof, so the Beginner takes him to where the TARDIS was last at before landing during the Blitz (The War and the Time Crack).
Landing in Rome, the duo encountered the Rock Kind, and a roman guard who was guarding the Doctor's TARDIS. The Doctor was sent back to his time of 'death'. (TARDIS in Rome, The Impossible Astronaut, The Wedding of River Song).
Behind the scenes Edit
Beginner's Adventures is a spin-off based on the hugely successful and popular show Doctor Who, where the Doctor is the main character of the show.
The First Doctor was initially going to meet the Beginner in his first incarnation in a story titled UFO, and in his timeline it would take place shortly after their crash in Encounters. This plot point was instead used in When Worlds Collide where he meets him to apologise for crashing in the Beginner's third incarnation instead, leading to their adventure.