Perhaps we should start with the usual simplification that 'Hebrew writes only consonants'; the Hebrew letters corresponding to Y, H, W, H are written.
But not all Hebrew written letters are actually consonants in the phonetic sense: in most English uses, for instance, Y and W stand for semi- or half-consonants" (not sure of the English terminology here), and it was most likely also the case in ancient Hebrew. Moreover, in Biblical (and even more in DSS) Hebrew a number of letters can also work as matres lectionis, i.e. as a graphic reminder of (or substitute for) a full vowel; in that case Y can stand for "i" or "e", W for "o" or "u", H for "a" or "e". It is an either/or system: either the letter stands for its own (semi-)consonantic value, OR for the vowel it substitutes -- not both -- a fact which is often missed by those who try to deduce the vowels of the Tetragrammaton from the written letters, while retaining their (semi-)consonantic value.
Now when you transliterate Hebrew into Greek you find yourself with a problem; neither the semi-consonantic Y or W nor the aspirate H exist as separate letters. To transliterate a name like Yahweh you will likely have to use four Greek vowels: i-a-u-e (or more, e.g. i-a-ou-ai); if the Hebrew equivalent to W is read as a fricative (V) as is the case in later, especally Eastern-European Hebrew, you may include the consonant beta: i-a-b-e etc. (in late Greek beta tends to be pronounced as "v" as well). And that the divine name in Greek transliteration seems to consist of four vowels (even though at least two of them may have originally stood for semi-consonants just as Y and W) lends itself to speculation in a Hellenistic setting (cf. Plato on the "superiority" of vowels over consonants, and the vocalic invocations in Gnostic texts of the Nag Hammadi library for instance).