There was a time when it was Baddacks special, which takes place long before the Dragon Ball story began, was considered canon. On that occasion, the Saiyan had just completed a mission to the planet Kanassa and was watching his newborn son with ridiculous force before he set off for the planet Meat.
Until recently that was the first meeting between father and son, However, Dragon Ball Minus first and Dragon Ball Super then radically changed Bardock's history and the planet Vegeta. Chapter 77 of the Midquel manga reveals the first real meeting between Goku and Bardock.
Back from a long mission, Gine greets her husband in the house and while a little raditz is playing in front of her house, the Saiyan woman takes Baddack back with her to show him an incubator that contains little Goku. Same hair as his dad and looks we've seen in the past, with Gine asking Baddack to name him. At this time the name Kakarotto was born and it is also this moment that aroused compassion in the Saiyan who chose not to kill cereal and granolah during the attack on the planet Grain.
In short, the first meeting between Bardock and Goku has radically changed the life of the Saiyan warrior in more ways than one.
