OP, you might well find Pink Brain, Blue Brain by Lise Elliot an interesting read. She's a neuroscientist whose field of expertise is brain plasticity in early infancy. In a nutshell, her argument is this: insofar as some (some, by no means all) studies have shown a small cognitive difference between the average of the female population and the average of the male population, this difference has a very small d-value (typically below 0.5), and because the brain is so plastic in early infancy through to 5 years, and we know from observational psychological studies that male and female infants and children are treated differently by the adults around them, it is impossible in principle to tell whether these tiny differences are due to nature or nurture.
The picture is a plot of different d-values - as you can see, for d-values less than 0.5, the overlap between the populations is huge. So, say (just making up an example - my copy of the book is on loan to a friend) the average age at which a female toddler gets to a vocabulary of 20 words is 18 months, and the average age for a male toddler is 18 months and 2 weeks - you might well find that 48% of boys still reach that 20 word milestone before the average for girls. Tiny difference, not worth basing your future educational practises and employment practises on.
The "treating boys and girls differently" example I particularly remember is the crawling babies (about 9 months) and ramps test. When the babies were put in a room with care workers who didn't know their sex and let loose on ramps of varying steepness, there was no difference in the steepness of ramps the sexes could tackle. When put back in the room with their mothers, mothers of boy babies tended (on average) to correctly estimate the steepest ramp their child could tackle and leave them to get on with it, while mothers of girls tended (on average) to underestimate the steepness their child could tackle, and intervene and lift them off ramps they were perfectly safe and happy to explore. Multiply this effect over all the various small but significant sex-stereotypes we all carry around, and impose it on children whose brains are developing in response to the stimuli around them, stimuli which in turn are being selected and amplified or suppressed by the adults caring for them, and you get a situation where there is no way of knowing of a cognitive sex difference measured in adulthood whether it's innate or down to social conditioning.
Oh, and remember when people pop up to say "I thought it was nurture until my (single, unrepresentative sample of a) child did XYZ" that the plural of anecdote is not data!