This approach works for me (using hooks):
First of all define the options you need in a variable:
const genderOptions = [{ label: 'M' }, { label: 'V' }];
Second you can define a hook to store the selected value (for example store it in session storage for when the page refreshes, or use useState directly):
const age = useSessionStorage('age', '');
Next you can define your Autocomplete as follows (notice the default values in value and getOptionLabel, if you omit those you'll get those controlled to uncontrolled warnings):
<Autocomplete
id="id"
options={ageOptions}
getOptionLabel={option => option.label || ""}
value={ageOptions.find(v => v.label === age[0]) || {}} // since we have objects in our options array, this needs to be a object as well
onInputChange={(_, v) => age[1](v)}
renderInput={params => (
<TextField {...params} label="Leeftijd" variant="outlined" />
)}
/>