Does “they had not hunted long before they had a sight of him” mean “they soon found the stag”?
Tumnus came down river and brought them news that the White Stag had once more appeared in his parts—the White Stag who would give you wishes if you caught him. So these two Kings and two Queens with the principal members of their court, rode a-hunting with horns and hounds in the Western Woods to follow the White Stag. And they had not hunted long before they had a sight of him. And he led them a great pace over rough and smooth and through thick and thin, till the horses of all the courtiers were tired out and only these four were still following.