Gender at birth
Additionally, since gender refers to behaviour and societal roles, I don't think "gender at birth" makes sense, given that all babies act pretty much the same for the first few months. You would be better to phrase your question as "gene-determined sex", which is for now unchangeable.
that's not actually true - http://www.city.ac.uk/news/2016/july/infants-prefer-toys-typ...
there's a lot of evidence to suggest that choice of toy is at least partially influenced by sex.
I do not believe you