Explaining a bit more, one reference that comes to my mind is that of the Japhetic race in the Bible.
If there's something in the Bible which is more of a Near East product of non-IE culture, surely there must be something in the larger IE tradition.
This is way too much asked to answer. What time period are you talking about? At 0 CE, for example, there were really just three Germanic languages: East Germanic, and the more closely interrelated North and West Germanic. And they certainly knew their languages were related, the three branches were very intelligible at that point. There was never a moment where the Germanic languages were not assumed to be related; and later works in the Middle and Early Modern Ages tried to reconcile them with Latin, Greek, and Slavic (cf. Lipsius and Marcus Zuerius van Boxhorn).
Ancient Latins and Greeks knew their languages were related (although they though Latin was a descendant of Greek, which isn't true), but we have no evidence they thought that about other languages.
So you need to be more clear.
I don't entirely understand your point about the Bible, but it should be noted that Hebrew is not an Indo-European language, but instead is a Semitic Language, which belongs to the Afro-Asiatic group of languages.