I think a helpful human translator might use singular "they" in cases where the sex can probably not be known (for example, if it's a reference to a hypothetical person) and there is little danger of confusion with plural "they", and "he/she" in other cases (for example if the person requesting the translation might know the sex and be able to fill it in for themselves).

Those criteria also align roughly with the acceptability of singular "they" in modern British English: a sentence like "everyone should mind their own business" is totally normal and standard and always has been; a sentence like "the unidentified miscreant left their cup on the table" will seem a bit strange to some people; a sentence like "Chris ate their lunch" will seem strange to a lot of people.

I wouldn't expect Google Translate to be capable of such cleverness so a simpler solution would be needed.