In Homer's Odyssey
16.154-163 (tr. A.T. Murray, rev. George E. Dimock), the goddess Athena makes an appearance, but she is not visible to everyone:
He spoke, and sent the swineherd on his way. He took his sandals in his hands, and bound them beneath his feet and went into the city. Nor was Athena unaware that the swineherd Eumaeus was gone from the farmstead, but she drew near in the likeness of a woman, beautiful and tall, and skilled in glorious handiwork. And she stood over against the door of the hut, showing herself to Odysseus, but Telemachus did not see her before him, or notice her; for it is not at all the case that the gods appear in manifest presence to all. But Odysseus saw her, and the dogs, and they did not bark, but with whining slunk in fear to the farther part of the farmstead.
ἦ ῥα καὶ ὦρσε συφορβόν· ὁ δ᾽ εἵλετο χερσὶ πέδιλα,
δησάμενος δ᾽ ὑπὸ ποσσὶ πόλινδ᾽ ἴεν. οὐδ᾽ ἄρ᾽ Ἀθήνην
λῆθεν ἀπὸ σταθμοῖο κιὼν Εὔμαιος ὑφορβός,
ἀλλ᾽ ἥ γε σχεδὸν ἦλθε· δέμας δ᾽ ἤϊκτο γυναικὶ
καλῇ τε μεγάλῃ τε καὶ ἀγλαὰ ἔργα ἰδυίῃ.
στῆ δὲ κατ᾽ ἀντίθυρον κλισίης Ὀδυσῆϊ φανεῖσα·
οὐδ᾽ ἄρα Τηλέμαχος ἴδεν ἀντίον οὐδ᾽ ἐνόησεν,
οὐ γὰρ πω πάντεσσι θεοὶ φαίνονται ἐναργεῖς,
ἀλλ᾽ Ὀδυσεύς τε κύνες τε ἴδον, καί ῥ᾽ οὐχ ὑλάοντο
κνυζηθμῷ δ᾽ ἑτέρωσε διὰ σταθμοῖο φόβηθεν.
In Sophocles' Ajax
14-17 (tr. Hugh Lloyd-Jones), Athena again manifests herself to Odysseus. But this time he can only hear her, not see her:
Voice of Athena, dearest of the gods to me, how easily do I hear your words and grasp them with my mind, even if I cannot see you, as though a Tyrrhenian trumpet spoke with brazen mouth.
ὦ φθέγμ᾽ Ἀθάνας, φιλτάτης ἐμοὶ θεῶν,
ὡς εὐμαθές σου, κἂν ἄποπτος ᾖς ὅμως,
φώνημ᾽ ἀκούω καὶ ξυναρπάζω φρενὶ
χαλκοστόμου κώδωνος ὡς Τυρσηνικῆς.