bubbles There are differences between men and women. There is not much evidence if any that those difference exist in babies or toddlers.
Its almost impossible to separate out any actually genetic effects from the hugely more important societal stereotyping effects.
I have two favourite experiments that demonstrate this.
Firstly the experiment where a child is deliberately dressed as the opposite gender and left playing in a room of toys supervised by an adult that doesn't know them.
The adult interacts with the child and plays with them and the toys. Almost universally the toys used match the gender stereotype the adult sees and not the gender stereotype of the child.
So a male child will end up playing almost exclusively with dolls and teddies and a female child will end up playing almost exclusively with trains and robots.
So when you look at girls and see them mostly playing with dolls, you need to realise that this preference is almost entirely chosen by the adults supervising them in their formative years and not by the themselves children.
Secondly people watched young toddlers doing a climbing obstacle course. The actual physical abilities of the boys and girls were identical. The perceived ability of the children by their parents was very biased in that parents thought the male children were much better at climbing than the female children. They also observed many many cases in which adults prevented the female children from climbing something they could actually climb perfectly well, while allowing the male children to get on with it.
When the children are a little older you begin to see differences in actual ability which are almost certainly due to girls not being allowed to progress as rapidly as boys by their own parents.
All of this points towards the differences in the sexes being something that is in the majority imposed by adults expectations of children and not their own abilities or preferences at all.