If you come up with a genetic algorithm scaffolding to affect both the architecture and the training algorithm, and then you instantiate it in an artificial selection environment, and you also give it trillions generations to evolve evolvability just right (as life had for billions of years) then the answer is yes, I'm certain it will and probably much sooner than we did.
Also, I think there is a very high chance that given an existing LLM architecture there exists a set of weights that would manifest a true intelligence immediately upon instantiation (with anterograde amnesia). Finding this set of weights is the problem.