I think you have wrong assumptions about grammatical gender. Grammatical gender is a grammatical feature, not a biological. German nouns have a grammatical gender. People don't. People have a biological sexus. Normally biological sexus and grammatical gender match, but there are also many exceptions.
The most prominent exception is the noun »Mädchen« which is a neuter (not neutral!) noun but it means »girl«:
Das Mädchen ist schön. Es hat langes Haar.
The girl is beautiful. She has long hair.
As you can see, in German it is perfectly normal to often use the neuter pronoun »es« to refer to a female person. The grammatical gender of the noun that a pronoun refers to, in this case "das Mädchen", takes precedence over the sexus/gender of the person.
English nouns do not have any gender. So, in English, pronouns can't refer to the grammatical gender of a noun. Instead they refer to the sexus of the person or thing that is named by the noun. This is a different mechanism than in German. And if this person or thing doesn't have a biological gender, you use the pronoun »they« or »it« in English. In German we don't care about the biological sexus of people when we use pronouns. We care about the grammatical gender of nouns.
I give you another example to make it more clear: In German you can use these three noun for an old shabby limousine:
- das Auto (neuter)
This is the standard-translation for "the car" and matches for any car, including old shabby limousines.
- der Wagen (masculine)
The original meaning was "carriage" or "wagon" but since there are cars, it also is used as a synonym for "Auto", especially when the car is bigger, so German »Wagen« fits well for a limousine.
- die Karre (feminine)
The original meaning was "cart", "barrow" or "trolley" but it also is another synonym for "Auto", especially when the car is rusty, old and shabby.
So, for a shabby and rusty limousine you can use all three nouns:
neuter noun needs neuter pronoun: Das Auto ist alt. Es ist rostig.
masculine noun needs masculine pronoun: Der Wagen ist alt. Er ist rostig.
feminine noun needs feminine pronoun: Die Karre ist alt. Sie ist rostig.
What does this mean for your question?
German doesn't have any gender-neutral words. Each word has one of these three grammatical genders:
- neuter - Das Auto (car), das Messer (knife), das Mädchen (girl), das Weib (woman, wixen), das Kind (child), das Genie (genius)
- maskuline - Der Wagen (big car), der Löffel (spoon), der Mann (man), der Champion (champion)
- feminine - Die Karre (shabby car), die Gabel (fork), die Frau (woman), die Koryphäe (expert)
So, when ever you talk about a person, you have to use a noun to describe this person, and any pronoun you use must have the same grammatical gender as this noun. This is even true if the noun itself is not said or written. This may lead to ambiguous situations, where it is not really clear, which pronoun to use, and to use a pronoun that matches to the biological sexus is often a good idea in such a situation. But still if you do so, the pronoun in fact matches to a noun that is in the mind of the speaker, even if they don't use this noun.
Example:
A person, about 5 years old, with pigtails, wearing a pink dress, playing with a doll and named »Emma« by the other persons in the room hits her leg and starts crying. Someone who watches the scene could say:
Es hat sich verletzt.
So you know, the speaker refers to a neuter noun when they think about this person. This might be »das Mädchen« (the girl) oder »das Kind« (the child) which are both neuter nouns, also the person is female.
Another example:
In German you could say:
Die Koryphäe weis mehr als alle anderen über dieses Fachgebiet.
Although the noun die Koryphäe is a feminine noun, this does not mean, that the person meant by this word has to be female. Also a male person can be eine Koryphäe. The same is true for the masculine noun »der Champion« this can be a female or a male person.
Das Genie ist heute bei und zu Gast. Es hält einen Vortrag über Quantenkryptographie.
The word »das Genie« is neuter. It can mean a female or a male person.
Another situation is when you don't know the biological sexus of a person. Also in this case you have to use a pronoun that matches with with the noun you use to discribe this person:
In der dunklen Nische stand eine vermummte Gestalt. Gleich darauf verschwand sie.
A hooded figure stood in the dark alcove. Immediately after that they disappeared.
Here you have to use sie because this pronoun refers to the noun »Gestalt« which is a feminine noun. But the reader still doesn't know the biological sexus of this hooded figure. In English you have to use the singular they in such a case, because in English you always refer to the biological sexus of a person, but when you don't know it, you can't use he or she, so you use they.
Some exceptions:
Since about 1970/1980 German speaking people more and more begin to use pronouns that match with the biological sexus if a word refers to a person and the grammatical gender of the noun and the biological sexus differ, and since about 20 years it no longer is considered to be wrong:
- was always correct and still is correct:
Das Mädchen ist schön. Es hat langes Haar.
The girl is beautiful. She has long hair.
- also correct since about 2000:
Das Mädchen ist schön. Sie hat langes Haar.
There are some German words that have two genders. See this list. That means, that you can choose a gender, but once you have chosen one, you should stick with it.
But there is no Gernan noun without any gender. This is impossible in German. (In English every noun has no grammatical gender.)