The word 'agape' existed before Christianity, and meant something broadly similar - some kind of love, not necessarily romantic or sexual.
It seems to me that the precise nuance varied a lot over time. For example, the Septuagint, the translation of the Hebrew scriptures into Greek in ~200 BC, uses it for all forms of love, including in the extremely saucy Song of Solomon [1]. The 20th Delphic maxim (~600 BC) is "Φιλίαν ἀγάπα", which means something like "desire friendship" [2]. In the Odyssey (~700 BC), Eurycleia describes Telemachus as "μοῦνος ἐὼν ἀγαπητός", meaning Odysseus's "only and beloved" son [3].