If some dfs are able to do it as their base ability, then why not the Soul Fruit and Big Mom?
We can't just pick and choose whichever feels convenient lol.
If you want to go down that route, then do it for all examples.
No, it has never been explained that Gladius or Diamante's ability can affect their surroundings from the start.
They were just able to do it from the start. We don't know whether it's Awakening or not.
Their fruits turn them into Flag Man & Rupture man respectively, their ability can be awakening for all we know.
And it's not like Oda never did it with other characters;
In Skypeia, Enel wasn't the only one with Mantra, his Priests had it as well.
In Enies Lobby, Lucci wasn't the only Rokushiki master, the rest of CP-9 also had Rokushiki abilities.
In Fishman Island, Hody alone didn't take Steroids, his subordinates also did.
In a similar way, it can easily be that Doflamingo alone wasn't awakened, his subordinates were also Awakened df users.
Corazon is an undebatable argument though.
Until his last moments he didn't "assign" the silent bubble to himself.
In his final moment, he did it onto Law, before that he's never done it.
Even then he talks about being alive until Law gets out of range that him crying won't be audible to Doffy.
The way his fruit works also works just like Kid's fruit for example,
Kid's fruit turns himself into a Magnet Man as a base ability & his Awakening is to "Assign" such Magnetism to others.
Rocinante's fruit turns himself into a Silent Man as a base ability & his Awakening is to "Assign" that Silent Bubble to others.
So what gives?