Transcriptions into Latin
While there are no transcriptions from the time of Homer (since the alphabet didn't exist yet), these provide good evidence that the change from
[ef] happened after the Classical period. A brief search turns up examples like Autolycon, Baucus, and Caunus in the Metamorphoses, as well as borrowed words like centaurus. We can be reasonably confident that these borrowings reflect the pronunciation rather than the spelling because they use Latin U rather than the borrowed letter Y.
Greek phonological changes
There's also evidence that αυ and ευ acted as single units within Homeric-era Greek, rather than as sequences of a vowel and a consonant. The second element in these diphthongs survived the loss of independent digamma, for example, which disappeared even after alpha and epsilon: ἀέκητι < *a-wek-, ἀϊδνός < *a-wid-. This sort of cohesion seems much more likely for diphthongs with two (semi)vocalic elements, than for a vowel followed by a fricative. (It also implies an underlying representation like
/au/ rather than
/aw/ at this time, which is even less likely to turn into
In the end, we can't be certain
As Unbrutal_Russian mentions in the comments, it's impossible to be certain. The best evidence comes from transcriptions, which didn't happen until centuries later, and there's no way to prove (for example) that it didn't change from
[af] before Homer's time and back to
[aw] again after.
However, even if we can't be certain, we have no reason to suppose such a change either; for all practical purposes, such as recitations of Homer, I would assume