Goku didn't get stalled...

[SSJ2]

What if Goku wasn't stalled by Dr. Briefs before taking off for Namek? If he took off right away, could he have been there when the entire Ginyu Force were together (before they fought Vegeta/Gohan/Krillin) including Ginyu? If so, how would Goku handle the situation against the entire Ginyu Force?

 

[Captain Cadaver]

He only seemed to be stalled for a minute or so, so it wouldn't make much of a difference, seeing as how there was a 2 minute gap between Reacoom beating Vegeta and Goku's arrival. Vegeta still gains his Zenkai, whilst Gohan doesn't. However, his potential unlock constantly raising his power would still allow him to fight against Goku Ginyu and be considered of use against Freeza, considering Kuririn made similar gains. All that'll change is Gohan being minimally weaker than in the main timeline, which will be corrected once he gets the rage boost against 2nd form Freeza.

 

[Jeff Styles]

Wasn't it just for a few seconds? I remember Dr. Briefs telling Goku about the spaceship, the buttons for the gravity chamber, the food, how to start the ship, etc.

The same. Goku would defeat Jeice and the other three. Ginyu would be interested in Goku hiding his power. The differences I see are

- Vegeta wouldn't get his zenkai
- Goku wouldn't have to use the 3 senzus to heal Vegeta, Gohan, and Kuririn
- Vegeta would kill Jeice and the others and injury Ginyu (Goku's body)
- Goku would eat a senzu after he get his body back.
- Goku would join the fight against Freeza sooner rather than later

 

[Captain Cadaver]

- Vegeta wouldn't get his zenkai

He'd still gain it. By the time Goku's ship noted it would be 2 minutes until arriving on Planet Namek, Vegeta had already suffered all the injuries Reacoom would deal him.

- Goku would join the fight against Freeza sooner rather than later

This is something I overlooked and a pretty drastic one. With extra Senzu, Goku would have his post-Zenkai gains immediately, meaning Freeza would immediately go to his true form. Whilst this changes nothing from a plot perspective, it does change character development a little, as Vegeta wouldn't have his death speech to allow the others to open up to him as an ally and he likely wouldn't be accepted to stay at Capsule Corp., making him more of a loner character like Piccolo. I imagine he'd still stay at Capsule Corp for gravity training in the 3 years training, but it may mean Bulma would take longer to fall for Vegeta, meaning Trunks would probably end up 1-2 years younger. This doesn't change much in the plot though. Seeing Goku eclipse him far earlier would likely fuel Vegeta's desire to surpass him far earlier and of greater extent since he didn't have the saviour aspect to a near death Vegeta to have Vegeta view him positively. This may mean Vegeta's strength is greater than in the main timeline from thereon, though likely not by enough to change the plot.
I still think Piccolo would fuse with Nail, as I imagine Goku would still stick with the group to protect them rather than immediately chase down Freeza to challenge him. I also don't think the wishes would change either, seeing as how all it'd mean is that Vegeta wouldn't be able to stress his claim of immortality when Goku was far stronger.

So, still not much changes.

 

[Jeff Styles]

He'd still gain it. By the time Goku's ship noted it would be 2 minutes until arriving on Planet Namek, Vegeta had already suffered all the injuries Reacoom would deal him.

I was actually going by SSJ2's question regarding how Goku would handle the entire Ginyu Force. Which would happens before Vegeta got injury since Ginyu left with the DBs to Freeza's spaceship.

 

[withheldforprivacy]

Assuming Goku arrives before the battles commence...
Considering none of the Ginyus knows Goku, they group him with
the weaklings in their minds, so Guldo attacks Gohan, Krillin and
Goku at the same time. I expect Goku to be too relaxed and fall
for Guldo's paralysis just like Gohan and Krillin did. Vegeta beheads
Guldo and saves them.
Round 2, Vegeta fights Recoome like in canon. After Vegeta is
defeated, Goku busts in and defeats Ginyus like in canon. He uses
one of the three senzus to heal Vegeta. Ginyu swap saga goes like
in canon. After Ginyu gets frogged, Goku uses one of the two
senzus to heal himself.
With Goku at full power, Vegeta cannot demand any of the wishes
for himself, so the gang uses the third wish to bring Piccolo right
where they are. Freeza shows up. Two cases...

1. Goku defeats Freeza before he can transform
They all get back to Earth. Trunks warns them about Androids
and reveals the Super Saiyan form to them.
Vegeta makes up for the one less zenkai when he trains till
he reaches his limits at gravity chamber. Gohan is probably
weaker than in canon, due to two less zenkais. Androids Saga
goes as we know. Piccolo is weaker than in canon, because he
didn't fuse with Nail.
Piccolo gets absorbed by Cell at Ginger. When Androids arrive
at Kame House, Krillin and Tenshinhan try to stall them. Cell
shows up. Tenshinhan is killed, because Goku can't teleport
there to save him. Gohan makes up for the two less zenkais
when he trains to his limit at ROSAT.
Cell Games end with Cell destroying Earth when he attempts
suicide. Then, he goes to explore the universe.
Beerus wakes up. With Namek dragonballs, they find out about
Super Saiyan God secret. Cell produces 5 Cell Jrs, performs
the ritual and fights Beerus. Then, he becomes his student
and takes part in U6 tournament. Considering Trunks died at
Cell Games, Zamasu's zero mortal plan succeeds.

2. Goku is so stupid that he waits for Freeza to go through all
transformations
50% Freeza stomps Goku. When Goku has reached near death,
he decides to take the last senzu. But, since he has already
reached his pre SSJ limit, he gets no zenkai and still gets
trashed. After that, things go like in canon.
The only thing that changes at Androids/Cell saga is Piccolo
getting absorbed by Cell at Ginger (because he hasn't fused
with Nail). He's brought back after Cell Games.
After that, everything is the same, unless Piccolo not having
fused with Nail affects his performance at TOP, so Universe 7
gets erased forever or till Jiren decides to bring it back with
Super Dragonballs.