It would probably take him a while to do so, considering it took him 3 years in the main timeline with the additional motivation of Trunks being a Super Saiyan too humiliating him. For the sake of the scenario, we'll say he achieves it in one year. Whether he arrives before or after Freeza is irrelevant as either Goku would immediately use Shunkan Ido to get to Earth and defeat him or Vegeta would fight Freeza and Cold, likely only being able to hold out until Goku arrived. In either case, Vegeta would calm down and see he still has to train. With his far more aggressive attitude and having not stayed at Capsule Corp. a year as in the manga, it's unlikely Bulma would've become attracted to him and Trunks isn't born.
This changes the future timeline somewhat as it's more likely that being Earth's last hope, Gohan wouldn't rush into battle against #17 and #18 and would instead wait for Bulma to build the Time Machine. This would either result in a scenario where he simply takes Trunks' role, or one I've went into in other What-Ifs in which he stays with his family for training that allows them to defeat #19 and #20, Gohan destroys the lab and Cell is eventually killed due to not being able to become perfect.
In the latter case, Dabura would be a major threat and even assuming Gohan and Goten beat him after training on the Kaioshinkai a long time, Freeza would still kill everyone after his revival due to the lack of necessary people for the God ritual (unless someone wishes for Tarble to be teleported to Earth in which case Super goes near enough the same until the Moro Arc).
In the scenario closer to the main timeline, the lack of Trunks for fusion would cause Goku to be fully intent on destroying Boo and successful in this. As for how this affects Super, Goku and Vegeta being dead would likely cause Beerus to stay asleep as in Future Trunks' timeline. How things go after this depends on Sorbet's intel, either:
1. Sorbet still believes Goku is on Earth. Freeza trains for 4 months and kills everyone on Earth after making his GAINZ, unless.
2. Sorbet is aware Goku and Vegeta are dead, causing Freeza to be overconfident in travelling to Earth and being easily dispatched. Most of Super doesn't happen until Moro breaks out of prison and causes havoc, likely causing Beerus to be woken up to deal with him before going back to sleep. That said, most of Super's events in general (thankfully) don't happen.
