There's no such thing as 'innate' intelligence in the sense of not changing over time. Trivially, your IQ is benchmarked against a norm of people your own age, with the absolute value of correct results changing considerably with age (typically rising steadily until ~25 before declining). There are also techniques like the dual n-back that show at least short term changes to IQ tests.
But brains are plastic and ever changing, learning new skills strengths connections and forms real physical changes in the structure of the brain. For example someone could start out with terrible visual spatial skills, but through practice their brain adapts to improve so that it does not need to constantly keep expending do much energy on a task it regularly encounters.
There is no reason to believe that regions of the brain often tested in IQ tests can't develop overtime increasing ones score. Sure it almost never happens since most people never engage in activities that would strengthen it, but it's silly to think it can't.
Innate intelligence assumes the brain is static and cannot change, which has been proven to be false.
> innate intelligence: something that does not change over time or by learning
Isn't it a contradictory definition? If someone is intelligent then it will learn to improve on a test, otherwise, it's not intelligent. Maybe we should take the gradient of the IQ scores.
In fact that's the conclusion of the study here.