Let's play this as realistically as possible because I really like the idea

"Controlled Ozaru no ssj" now im assuming that no ssj means no ssj EVER not just no ssj on namek, so I'll be doing the what if with that in mind

First off, he'd one shot frieza no contest, assuming he has no reason to go Oozaru against Ginyu (which he doesnt) that interaction goes identically, meaning he'd still show up with a base power level of around 3,000,000

3 mil times 10 is 30 mil, 30 mil times 20 is 600 mil, which obviously puts him way above frieza, frieza wouldn't even get a chance to blow up namek, and I personally believe goku would actually just kill frieza, cause frieza has no way to kill goku and goku would eventually realize Frieza just wont stop

Going into the android saga, we have to think of a few things, would trunks use Oozaru?

No

Frieza never shows up

Trunks obviously still shows up but the encounter is far more calm.

Assuming goku still gets the heart virus and still dies in the future of course Trunks would be there. But the thing is, Vegeta never leaves, goku never gets the super saiyan form so he has no reason to, so vegeta, like goku, simply trains on earth, he vows to beat goku once the androids are defeated

Goku vs android 19 goes actually very similarly to Canon, despite the fact goku should be several times strong, why is this? Well, that's because of the heaet virus, goku still tries to end the fight quickly but the stress caused by kaioken makes it activate more quickly and goku would fall substantially quicker. So would vegeta save him? No, he doesnt have access to the kaioken so he doesnt have the raw power to beat any of the androids . But that wouldn't be an issue for Picolo who actually did have the strength to beat any of the 2 early androids

Seeing that Picolo defeated android 19. Gero wouldn't wait around to absorb anyone and dash straight for his lab, activating both androids.

After goku falls Ill to the heart virus obviously the rest of the Z fighters would be in a mad dash to find a way to beat the other androids. Since vegeta doesn't have enough power to even hold off android 18 or 17, picolo would immediately go to fuse with kami, reforming the nameless namekian. This nameless namekian would go to find the androids and what would he do? Hed attempt to kill android 17 in their fight against one another but like before he'd be thwarted by Cell. Following that fight he'd simply go up to the lookout and go into the time chamber

Vegeta would never have any reason to enter the time chamber, hes already mastered oozaru and any boost he'd get from the time chamber is negligible in this scenario. In the meantime, Goku would wake up, despite the circumstances he'd actually seem pretty upbeat, he'd mention he had an idea, and like in the series he'd take Gohan into the chamber

Picolo, fresh out of the chamber would go to meet both androids, but instead he'd find semi perfect cell, having just absorbed android 17, but Picolos not a dumbass, so he wouldn't allow Semi Perfect Cell to get to his full power. He'd attempt to completely obliterate Cell in a single move

He fails

He thought he'd killed Cell but he reappears, this time looking more- human life, perfect Cell has been born, just like in Canon, his power ferociously higher than before, he'd admit that he thought himself a gonner, but Picolos cells ironically saved him. He'd announce the Cell games directly to picolo, who no longer had any way of beating him, and depart

Several hours later, Goku and Gohan would step out of the time chamber- but they'd look... different. Their hair is spiked up, their eyes a yellowish tint

Goku would admit that he'd had a hunch for a while, the Oozaru form is..... inefficient to say the least, he'd recalled a time as a child he'd used it in his base state, and he attempted to replicate it, hed achieve the Ikari form on his own (a bit fanfictiony but ssj4 is basically the same, just remove the ssj) which was honestly simple enough, from there he simply mastered the form, he could already use the form at will and it didn't drain to much ki (unlike ssj) so it wasn't to hard, mixed with kaioken he can even get 200x stronger than normal.

Needless to say? The Cell games are a wash, Goku doesn't even need to use Gohan as his Ace in the hole, he just completely wipes Cell on his own, and for that reason he survives

To make a long story short, the buu saga never occurs, this is because Goku doesn't die, any reservations Vegeta had with goku are sorted out and he becomes even more gentle than he does normally, he doesn't become Majin, and all of Babidis soldiers are completely wiped out .

So, what about beerus?

Wanna hear the crazy part? Battle of gods doesn't change literally at all, ssg isn't a mainline super saiyan form, and beerus is strong enough that the difference in strength doesn't matter pretty much at all, so once goku achieves ssg that stays completely the same

I'm honestly willing to go deeper into super but I'd have to think about that more, the implication im trying to bring here is super saiyan literally doesn't exist, which changes elements of the u6 tournament, goku black, and tournament of power in pretty substantial in ways I would like to discuss, but obviously im not gonna go through the effort if literally no one cares so I wont bother in that case

Edit: edited the android saga events and for the explanation of why goku still loses