you need to convince the embassy your g/f has custody of the child and sole responsibility, your g/f could have both or just one of them..
women automatically get custody of under 7yrs old in almost all cases, but it is possible she could have custody but not sole responsibility, if she worked in another country or far away from the child, then the embassy could say who ever looks after the child day to day has sole responsibility. so sole responsibilty for some people could be difficult to prove.
and for example a father could have sole responsibilty in the eyes of the embassy but not custody ...
i think in your case your g/f shouldnt have a problem with sole responsibilty, the only problem if the bio father kicks up a fuss
