I had two things in mind, one general plot and he other character specific. 

General plot: probably padawans are the only Jedi remainin because they were evacuated before the last battle, while older Knights and masters stayed to fight. 

Character: I had in mind that my character was related to the owner of a Corellian shipyard, And after the great cataclysm he tries to go home, only to find it also destroyed. So he goes to one of their satellite yards to try to claim his inheritance. He republic remnants have commandeered all of the best ships, but he manage to get one.