To see how it came about we first have to dispose of one or two other sound changes en route from classical to modern. In Ancient Greek this stem took the form ἐκβαλ- ekbal- eɡˈbal-. The voicing assimilation of the consonant in the prefix ἐκ- ek-, making it voiced before a voiced consonant, appears to date from ancient times — see W. Sidney Allen’s Vox Graeca (CUP 1987) p. 18.
Ancient short unstressed vowels at the beginning of a word are lost (‘aphesis’) in Modern Greek. So for example the classical word ὄμμα ómma ‘eye’, or rather its diminutive ὀμμάτιον ommátion, stripped of its case ending -ον -on, loses its initial vowel to become Modern Greek μάτι máti ˈmati, still meaning ‘eye’. Classical ἐξερῶ ekserô ‘I will speak out’ (?) yields Modern aphetic
Classical voiced plosives became fricatives in Modern Greek (‘spirantization’). Loss of the initial vowel in ἐκβαλ- ekbal- eɡˈbal-, the example we started with, left an initial cluster ɡb-. This duly became ɣv-. It was this cluster that then underwent metathesis to give the modern vɣ-. I do not know when the metathesis happened in popular speech. It was resisted in the katharevousa (puristic) form of modern Greek.
No parallel metathesis seems to have happened to γδ- from classical ἐκδ-. Homer’s ἐκδύνω ekdúnō ‘I undress’ (as in modern English zoological ecdysis and fanciful ecdysiast) yields Modern Greek γδύνω ghdhíno ˈɣðino with the same meaning and unmetathesized.
I used to find Modern Greek useful for widening my students’ appreciation of the phonotactic possibilities of language, and there was usually a native speaker conveniently to hand. Clusters such as word-initial vɣ are not difficult, once you have mastered ɣ, but can seem very strange to speakers of other languages — all except those familiar with French, where initial vr vʁ is found in such everyday words as vrai ‘true’. From vʁ you just need to move the uvular articulation forward to the velar position.
Greek has other interesting word-initial clusters involving a fricative + obstruent: φτάνω ftáno ˈftano or φθάνω ftháno ˈfθano ‘I arrive’, βδομάδα vdhomádha vðoˈmaða ‘week’, χτές khtes xtes or χθές khthes xθes ‘yesterday’, χτυπώ khtypó xtiˈpo ‘I knock’, σχολείο skholeío sxoˈlio ‘school’, σγουρός sghourós zɣuˈros ‘curly’.
For really complex consonant clusters, however, you need to go to the Caucasian or Salishan languages. When I was teaching my phonological analysis class we never seemed to have any native speakers of those languages around.