The Super Saiyan 4 is one of the transformations that has been forgotten in time. It happened in the development of Dragon Ball GT, and since it was not part of the canon, it was discarded in the reboot of the adventures of the Z Warriors, in Dragon Ball Super.
Goku is the first to achieve it. He served to be able to face the threat of Baby, one of the most powerful and ruthless villains in the franchise. It was also the only way to return Kakarot to his adult body, since by a wish made to the Dragon Balls he was as a child.
Before that there was no indication that someone could go Super Saiyan 4; not even that legendary warrior that Frieza talks about in his stories. However, one of the elements of the transformation fuels a curious theory that Bardock may have been the first to achieve it.
What does the theory say?
The element that nourishes this hypothesis is that the warrior who achieves it goes to the most original instincts of the Saiyan race: those of the ape. So, whoever can master the Ozaru at its best takes the first step towards Super Saiyan 4. That’s what a review of is based on. Cinemas Comics to support his theory.
Mastering the Ozaru is not easy. Goku and Gohan are not able to control it as children and after they return to their natural forms they don’t remember anything. Bardock’s friends suffer the same consequence of not remembering what they did as giant apes.
But Bardock, just like we saw him with Vegeta in the first arc of Dragon Ball Z, yes he is able to keep his mind intact in this way. It is in Dragon Ball GT that Goku can master this transformation.
Super Saiyan 4 first goes through a Golden Ozaru stage. So, based on this explanation, the mentioned site explains how Bardock could have reached Super Saiyan 4 if he had not died.