S1 - Freeza is able to make training GAINZ and get his Golden form a lot quicker with a far better training partner than Tagoma, let's say 3 months. Cold recommends waiting until Freeza has fixed his stamina flaw though, so it still takes them 4 months. Cold makes great gains as well, though not being the prodigy his son is, I'd say he doesn't gain the Golden form (or an equivalent) and at best ends up as strong as True form Freeza. Without the stamina loss, Freeza beats Goku, with Vegeta then tagging in. Goku would probably wear Freeza down enough to give Vegeta an edge, though with Cold there as an extra distraction, Vegeta wouldn't be able to counter Sorbet's ring once Freeza gives the signal. The Saiyans are killed along with their allies, though Beerus orders Freeza to keep the Earthlings alive to make delicious food as offerings to him.
Freeza rebuilds his empire and defeats the Galactic Patrol, but is forced to be in the U6 tournament not long afterwards along with Cold. For the sake of the scenario, I'll say he's already recruited Broly by this point. As Beerus wouldn't think of using dead warriors, the team ends up being Freeza, Cold, Tagoma, Shisami and Broly. Freeza is defeated by Hit and without Paragus' death to fuel him, Broly loses as well when his Wrath mode is the most he can bring out. The Earths are switched. Zamasu's decision is influenced by Freeza's sadistic torturing of his weaker opponents such as Cabba on GodTube, so we instead get Freeza Black and Trunks escaping to a barren Earth to give his story an even bleaker end.
ToP never happens and Freeza is given no incentive to kill Paragus, so the Broly movie events don't happen either.
S2 - Cold would know not to mess with Goku after hearing he even killed Majin Boo and wouldn't think about training. He'd instead rebuild his empire in space out of the radar of the Galactic Patrol in case they brought word to Goku. The story remains the same up until the ToP where Cold is found by Shin and brought on as a member of the team. Being perhaps the weakest fighter there, however, he's quickly beaten and the lack of Freeza leads to Jiren winning anime-wise and being beaten by #17 manga-wise.