‘They/them’ has been used for singular people for centuries.
The Oxford English Dictionary traces singular they back to 1375, where it appears in the medieval romance William and the Werewolf. Except for the old-style language of that poem, its use of singular they to refer to an unnamed person seems very modern. Here’s the Middle English version: ‘Hastely hiȝed eche . . . þei neyȝþed so neiȝh . . . þere william & his worþi lef were liand i-fere.’ In modern English, that’s: ‘Each man hurried . . . till they drew near . . . where William and his darling were lying together.’