Sure the manga barely started before the anime DBS show, but it’s more complicated than that, for example

the movie …fandom.com/…/Dragon_Ball_Z:_Battle_of_Gods

the manga …fandom.com/…/God_of_Destruction's_Premonition

The movie was released March 30, 2013, but the manga didn’t start until June 24, 2016.

Although it seems there was a “promotional” manga that came out earlier, it is not THE manga en.wikipedia.org/…/Dragon_Ball_Z:_Battle_of_Gods#…

And it appears to be an adaptation of the movie, not the other way around. In this case I guess you could say neither the anime nor the manga (nor the promotional manga) is the “original”, the movie is the original.

For Resurrection of F …fandom.com/…/Dragon_Ball_Z:_Resurrection_‘F’

There was again a promotional manga, but it was an adaptation of the movie, and it did not even show the ending. So again here the movie is the “original”. And then the DBS manga series skipped this saga.

dragonball.fandom.com/wiki/Golden_Frieza_Saga#Tri…

However the manga adaptation stops before the fight between Golden Frieza and Super Saiyan Blue Goku, to encourage readers to go see the film (thus Toyotarou may have also decided to not adapt the saga in the Dragon Ball Super manga for the same reasons the adaptation ends before Goku’s fight with Golden Frieza).

dragonball.fandom.com/wiki/Universe_6_Saga#Manga_…

The Universe 6 Saga ended May 1, 2016 in the anime, and June 21, 2016 in the manga, so the anime was ahead by the end of the saga.

dragonball.fandom.com/…/Universe_Survival_Saga#Ma…

The Universe Survival Saga started February 5, 2017 in the anime, and August 21, 2017 in the manga, so the anime was ahead again. And the anime finished sooner too: March 25, 2018 vs November 20, 2018.

(not sure if this arc will be getting remastered though)