Technically yes, but for all practical purposes no. Different clans of primates (chimpanzees iirc) have "innovated" distinct and novel ways to get food, specific to their clan. These are not innate, they are taught within the clan and passed down from generation to generation. With this, they share a common cultural knowledge and can preserve it into the future.
From a practical point of view, the speed of this "innovation" is glacial, but not all that different from the pace of human progress for most of our history.
So what makes us different? I'd argue that the evolution of speech/language provided the most important initial boost. With language, all cultural knowledge, including innovations, becomes so much easier to retain across generations.
WRT. the social part, I'm reminded of something 'lisper keeps saying - that the minimum viable reproductive unit for homo sapiens is a tribe or a village.
Shared fiction is nothing else than just shared knowledge. Without collecting and keeping your knowledge you can't go further, there's no basis for innovating further.