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If Humans Die Out, Octopuses Already Have the Chops to Build the Next Civilization, Scientist Claims
(www.popularmechanics.com)
Do we need to die for this to happen? 
It's real sad to me how all the other intelligent lifeforms on this planet are biologically limited in one way or another. Rats? Live a few years. Octopi? Live a few years. Dolphins? The fuck they gonna do with those flippers? Ravens? Ditto, but wings. They can't even masturbate. Humans hit the evolutionary jackpot.
Humans didn't evolve and then start using tools, our ancestors used crude tools, much like many of he species you listed occasionally do, which resulted in an evolutionary selection bias for those who could best make use of tools. Tool use created humans and it in time could create descendants of those other species who are much more capable of using tools.
Yeah, that is true. Still, primates at least had a pretty good base from which to work towards evolving to use tools - hands, relatively high intelligence, and decent lifespans. I don't even know how you'd go about giving a dolphin or ravens grippers. Octopi and rats have a decent base to work with in terms of grabbing things, but they would need to evolve to extend their lifetimes several times over before they could reasonably maintain a civilization.
Tbh as someone else said, it's most likely some other primate species would take over in the meantime since they're much closer.