U7
freeza wiped out 'all' the saiyans before one was strong enough and willing to challenge him...unknown to him was goku training since he was a baby to fight. goku fights raditz, nappa, and vegeta. goku and vegeta push each other to near death. goku is pushed emotionally to the brink after learning what freeza has done to his people, and seeing his best friend exploded. goku has to do everything to ensure his son's survival and goku becomes the one thing that could defeat freeza.
honestly we have no idea what was possible with U7 saiyans before goku and vegeta because the rest were destroyed. aside from vegeta we have no idea how strong the previous generations got aside from the fact they were weaker than base Freeza.

U6
saiyans are still alive and 'thriving' as far as we know. Cabba is a strong warrior as is Caulifla and by extension Kale. Seemingly no U6 has been pushed to the brink necessary to transform but find it necessary to become strong and continue to train. (due to storytelling only 3 saiyans are chosen for U6). Finally they meet U7 saiyans and learn to transform.

I'm saying we don't know their life stories but we know that they are saiyans and they train and train and train and were chosen to represent U6. if we watched a U6 tv series it would be them just training to get their base stronger and stronger.