Lying awake in the middle of the night, I suddenly thought of the older, mostly biblical word beget. This was originally be + get, similar to be + come and be + have. It is irregular, originally beget, begat, begot and later beget, begot, begotten (cf get, got, gotten (for some people) and forget, forgot, forgotten). It is most famously used in the King James/Authorised version of the bible (1611), specifically in chapter 1 of the gospel according to Matthew, where “Abraham begat Isaac; and Isaac begat Jacob; and Jacob begat Judas [Judah] and his brethren” and so on.
This translates the Greek word ἐγέννησεν, egénnēsen, the third-person singular aorist active indicative of γεννᾰ́ω, gennáō, 1. to beget, give birth to 2. to bring forth, produce, generate. We can hardly say that Abraham gave birth to Isaac, but we could easily say that Sarah did, except that the word is almost always used in relation to men. At the other end of Matthew’s genealogy, it does not say that Mary begat Jesus, but rather that Jesus was born of Mary, using the passive voice of the same Greek verb. (Compare 1 Chron 3, where “the sons of David, which were born unto him” are listed.)
Later versions use either begot or was the father of. The Good news bible/Today’s English version avoids the problem by using “the following ancestors are listed: Abraham, Isaac, Jacob, Judah and his brothers” and so on. Other possibilities are the very un-biblical father and sire (both of which started as nouns).
Google Ngrams shows that the heyday of beget in all its forms was the 1650s, after which there was a slow decline to modern times. Surprisingly, though, there has been a rise in usage (especially of begat) since the 1980s, which I can’t find or think of any reason for.
While researching for this post, I found a book by David Crystal titled Begat: The King James Bible and the English Language. Note that much of the language of the KJV comes from Tyndale (1526-30) and Coverdale (1535), and even the KJV’s original phraseology is in conscious imitation of the earlier style (and English had changed a lot in that almost a century.