AHA! Watching out for hidden H's.
Classical Greek did have a H sound ...well the last traces of one indicated by a ̔ over a vowel.
If a word has an initial HA sound you will see ἁ ἅ ἇ
Here's some words with an initial HA sound.
Ἁβρός Habros soft delicate pretty dainty luxurious
ἁγιάζω to hallow consecrate make holy
ἅιδης Hades the place and the god of
αἷμα Haemo - Blood
αἱρέω to chose
ἅλς Salt the sea
the two sea goddess Thetis and Amphitrite are called sea-born
ἅμα an adverb hama At Once or a Preposition with Dative at the same time (together) with
ἁμαρτάνω to miss fail go wrong err sin
ἁρπάζω ravish snatch seize take away carry off by force