Sheba is not imaginary. Saba was a real and wealthy south Arabian kingdom centred on Marib in what is now Yemen, known from its own inscriptions, from Assyrian records, and from classical writers who described the incense trade it controlled. Frankincense and myrrh, the goods the queen brings in the biblical account, grew there and almost nowhere else, and the caravan route north through the Hejaz to the Levant is well documented. A ruler of Saba sending a trade embassy to a rising kingdom that controlled the northern end of that route is entirely plausible in principle.
The difficulties are of date and of person. Saba's attested rulers are men, styled mukarrib, and the inscriptions that name them belong to a period later than the tenth century BCE where Solomon is conventionally placed. The archaeology of Marib and of the great dam does not yet reach far enough back to confirm a tenth century monarchy of the wealth the story requires, and no south Arabian text mentions a journey to Jerusalem. The Ethiopian identification, which places Sheba on the African side of the Red Sea, is a later development and is generally read as a national claim rather than a geographical one, though the Sabaean cultural presence in the Ethiopian highlands is real.
So the queen sits where a good deal of the world's religious literature sits, between a plausible setting and an unverifiable event. What is certain is her afterlife. She is invoked in three scriptures, made a saint of wisdom by Christian typology, given a name and a conversion by Islam, and made the ancestress of an imperial dynasty by Ethiopia, all from a passage of thirteen verses that does not tell us who she was.