Until Goku achieved the Super Saiyan technique, nobody knew for sure that it was possible. It was only considered a legend that a Saiyan would have such tremendous power, but still, Goku managed to beat all odds in his epic battle against Frieza on planet Namek.
Becoming a Super Saiyan surely wasn’t easy. Goku was beaten up so hard by Frieza until that moment that it’s a miracle how our hero remained standing. But the new Super Saiyan emerged due to a combination of both absolute necessity and a strong emotional trigger. Previously, Goku fired the Spirit Bomb at Frieza, but the intergalactic tyrant still couldn’t be defeated. Therefore, the great Saiyan realized that pretty much nothing could stop Frieza at that point. The next step was for the tyrant to kill Krillin, who was Goku’s best friend. Such events could mean only one thing: even that he was extremely exhausted, Goku achieved renewed powers to take down Frieza once and for all.
Of course, it was also needed for Goku to have the right strength for the transformation. But Vegeta was also very powerful at that point, although he was pretty much below his rival. But even so, we firmly believe that Vegeta was strong enough to go Super Saiyan instead of Goku on Namek. The Saiyan Prince also confronted Frieza before Goku did, and that’s when the first Super Saiyan in Dragon Ball Z could have emerged.
But as we said previously, becoming a Super Saiyan for the first time requires more than just being strong. An emotional trigger is needed, which would have been pretty complicated for Vegeta at that time since he was nothing but a good person. So what could have been the emotional trigger for making Vegeta a Super Saiyan?
Feeling the humiliation of being beaten by the exterminator of his race would have been the needed trigger
You may have noticed that Vegeta is a very arrogant guy. He also has nothing but extreme hatred for Frieza, and for good reasons. Frieza is the one who killed Vegeta’s father and his entire home planet, along with almost all of the other members of the Saiyan race.
Vegeta losing to Frieza is humiliating enough. Sure, you might say, “but Vegeta did lose to Frieza and he still didn’t become a Super Saiyan”. Indeed, that’s true, but we’re exploring an alternative scenario here. Vegeta could have managed that situation in a different way, or to say it in another way, the writers could. When the Saiyan Prince was severely injured by Frieza, he could have started to see flashbacks of his father and other members of his race. Those flashbacks could have motivated Vegeta enough to achieve new heights in terms of power and become a Super Saiyan for the first time. There’s no telling exactly how strong Vegeta would have been in such a situation, but he could have surely posed a threat to the evil emperor Frieza in his final form.
We even anticipate that for the sake of the plot, Super Saiyan Vegeta might have even won in the end against Frieza and revenge his fallen Saiyan race. And since Vegeta doesn’t share Goku’s taste for forgiveness, the Saiyan Prince would have even got the job done and not let Frieza escape planet Namek.
Vegeta himself became a Super Saiyan later in the Dragon Ball Z anime, and he didn’t seem to need any emotional trigger. That was, most probably, because such as in the case of Future Trunks and Goten, the Saiyan prince was already much stronger than Goku was at the moment of achieving the legendary transformation for the first time.