Every saiyan at birth has the chance to go SSJ if they trained enough and had the proper conditions to go ssj. For example, vegeta had the power but didn't have the need (stopped caring) to unlock the power to go ssj. Once he stopped caring about being stronger than goku it triggered within him and he was able to go ssj.
Goku and Vegeta were ssj's at the time their sons were conceived. It's logical they passed the trait down to their sons which made it easier for them to go SSJ as opposed to gohan who was conceived when goku had a PL of roughly 250 at the end of dragonball.
ok dog