Yes. Take 8 year old Luffy going solo against the bandits for insulting his friends. Or Ace as an 10 year old going against the Bluejam pirates.
Compare that to Coby, who is (almost) twice the age, 16 (!) and licking the boots of a fodder like Alvida because he pisses his pants at the thought of having his ass spanked. You are born with those qualities of a king, you inherit it. You can't be a crybaby scared of having your ass spanked as a 16 year old if you are born with these qualities.
Compare that to Coby, who is (almost) twice the age, 16 (!) and licking the boots of a fodder like Alvida because he pisses his pants at the thought of having his ass spanked. You are born with those qualities of a king, you inherit it. You can't be a crybaby scared of having your ass spanked as a 16 year old if you are born with these qualities.
Since you brought up the example of child Luffy insulting these bandits: Don't forget that Shanks already influenced Luffy at this moment positively. If there was no Shanks, Luffy would take a completely different path. Who knows when Luffy would even start training. Well, since there is also Garp, Luffy still would find a proper mentor and role model to show him the way.
Meanwhile, Coby had none of that until he was 16. He was a cowardly weak cabin boy who worked for a low level pirate. Now this was the moment when Coby's life got turned upside down: Luffy came, rescued him and became Coby's Shanks. He positively influenced Coby to pursue his dreams. Then Coby perfectly demonstrated his kingly ambitions to become an admiral in the future and these are the two factors:
1.) Luffy. Yes, Coby is a Luffy fanboy but at the same time, Luffy was also the catalyst for Coby pursuing his dream. As I said, he's like Shanks for Coby. Luffy is also basically a Shanks fanboy, let's not forget that. Coby's admiration towards Luffy doesn't contradict the fact that he has all the factors to unlock his own conqueror's haki.
2.) Garp was the next one. His mentor who showed him the ways of the navy. He was the one who taught Coby all that stuff and made him into a powerful navy soldier with great CoO (and CoA?). Similar to how Kuzan was a bum at the beginning but then started having same striking strength as Garp.
Coby needed the same training and he successed everything due to his ambitions. Not everyone can do that.
So yes, it isn't farfetched to think that Coby became far stronger during the 2.5 years when he consistently trained to steel his body and mind. Oda basically says that Coby is highly gifted with talent.
I still think that unlocking ACoC is too soon though. The basic stuff would be a better start, especially since ACoC is also linked to Ryuo.