You fail to consider one of the sciences used to create the inventions: the science of engineering. If you don't think that's a science, then you don't know squat. It involves several aspects, but regardless if it's chemical, structural, or electrical, all engineering boils down to mathematics. Our earliest ancestors had to deal with it. How did they make the earliest knives? Trial and error and observation. Long before we understood how to extract metals from rocks, our ancestors used rocks themselves to make their tools. But it wasn't just pick up a rock and use it as a knife. They had to experiment, just like in science class, to find which rocks made the best knives, how to shap those knives, and even how to keep them sharp. For that matter, even before knives, rocks were used as a weapon by hurling then at a possible opponent, or directly bludgeoning a person or dinner with one. How did they know that would kill their supper? Seeing a tribal member get hit in the head by a blunt object? Realizing that they could make a blunt object by using a stout tree branch. Eventually, they added a rock to the end for and early axe. All by following the principles of science.
Many creatures today use various scientific methods without understanding the scientific principles behind them.
I ask,can you name one modern invention that does have science at its core.