Broly went from below casual base Vegeta to comparable with SSJB Gogeta in one battle. Goku would already be stronger than everyone in OG Dragon Ball by the time Bulma finds him lol. Pilaf Saga practically wouldn't exist. Goku still trains with Roshi but gets a slight increase in strength while a big increase in skill, most likely, and he would master the Kamehameha on the first use he used to destroy a car I'd bet. Roshi/Jackie Chun wouldn't stand a chance and the tournament is a breeze. I could go over the rest of OG but you get the point.
In DBZ, I'd imagine Raditz would give Goku a surprise, but Goku still stomps without much issue. Assuming he trains hard for Nappa and Vegeta, they're fodder. No one on Earth dies as Goku wouldn't die to Raditz, also meaning Goku doesn't develop a connection with King Kai, nor does he learn the Kaioken or Spirit Bomb, and, even more importantly, negating the entire Namek Saga as they would have no reason to go there. Frieza would probably become immortal if he still goes to get the Namek Dragon Balls, but I don't wanna go over that scenario, Vegeta might die trying to sabotage him or just remain under Frieza's heel, as I would see Goku still sparing him. Etc. throughout Z.
Honestly, things only really get even remotely challenging around Super. Goku would give Beerus a pretty good fight on King Kai's planet, and Goku by this point could probably be even stronger than SSJG Goku. Keep in mind that Broly was already at least comparable to base Vegeta, who would be MUCH stronger than Super Saiyan God Goku when he fought Beerus. So Goku would probably satisfy Beerus even without taking on a godly form. Beerus I imagine would still go to Earth after incapacitating Goku due to powering up. But Goku wouldn't have spared Buu most likely, meaning that Beerus wouldn't get mad, and would already be satisfied from Goku's battle against him, so I don't see Super Saiyan God even making an appearance yet, but Goku and Vegeta would still get it due to training with Whis. RoF is a breeze. U6 Tournament just ends with Goku stomping everyone after getting back in the ring. Future Zamasu Arc...well, Goku Black would also have crazy potential, even without the addition of Broly's, so I'm not sure how that would go. ToP would still be difficult because of Jiren, but overall U7 would win without much trouble. Broly movie would be interesting as Broly would have equal potential to Goku, but I imagine that Goku doesn't even fuse with Vegeta. Vegeta just gets a round with Broly, before Goku comes in and finishes it up. He has a massive headstart on Broly, plus the same potential. And Moro arc I imagine wouldn't change too dramatically.