Not while using the standard Greek alphabet. There is no letter for the sound /h/; it is represented as a diacritic mark applied to the first letter of a word.
(For completeness, aspiration is not strictly restricted to the beginning of a word in classical-to-Byzantine Greek. It might be represented in one of three ways:
- At the beginning of a word, according to Byzantine convention, it is represented by an aspiration mark, discussed above. This can only occur if the word begins with a vowel, or with R. (All words beginning with R are aspirated.)
- Following a /p/, /t/, or /k/ sound, aspiration is represented by mutating the letter into an aspirated form. Unaspirated π becomes aspirated φ, τ becomes θ, κ becomes χ. By the time we're talking about Byzantine Greek, the "aspirated" letters have mostly mutated into other sounds. But for ancient Ancient Greek, they are aspirated forms.
- Doubled Rs have something special going on with them, and the Byzantines use a diacritic mark on the second R even though, obviously, it cannot occur at the beginning of a word. Again there is no contrast between "aspirated" and "unaspirated" double R; the aspiration is mandatory.
As you move into earlier stages of Greek, you lose the standardization of the alphabet; there are plenty of Greek inscriptions where the sound is represented by the glyph H.)
https://en.wikipedia.org/wiki/Unit_prefix#Unofficial_prefixe...
https://en.wikipedia.org/wiki/Hella#SI_prefix