This era in time shall take place with a slight difference with the Saiyans Vegeta, Radtiz, Tarble, and Broly have the same age as Goku during the time of Planet Vegeta's destruction and by the slightest stroke of fate where sent to Earth at the same time but not at the same place. Now the story can very with how you decide the young saiyans looking at the full moon either the Saiyans destroy the Earth as great apes or continue there stories in the dragon ball style, I prefer the second option with, Goku still lands with Grandpa Gohan, but the others land with important with other dragon ball characters Vegeta with Master Shen, Radtiz with Roshi, Tarble with the Briefs, and Broly to be found by pilaf to later be given to King Piccolo.