Perhaps, our ignorance is a little overbearing when we become adamant that our understanding is right.
The following references where γενεὰ is found in the following verses, Matthew 12:39, 16:4, 17:17, 24:34, Mark 8:12, 9:19, 13:30, Luke 9:41, 11:29, 11:29, 21:32 could just as easily be translated into the English word, "age" which has a duration of a thousand plus years. It is used in the LXX Greek translation of the OT in Genesis 15:16 and because the Jewish scholars could not get their laughing matter around a time period into their future of some 3,000 plus to 4,000 plus years, they forced this particular one verse prophecy back to the previous prophecy found in verse 13-14 of the same chapter with respect to Israel being taken out of Egypt. This has lead to the erroneous understanding that there were only four descendant generation born during Israel's time as a nation living in Egypt, whereas, the bible records that one family had ten descendant generations born in Egypt while they lived their.
Now if the Jewish translators can get the context of this one verse wrong and used the Greek word γενεὰ to represent the contextual meaning of the Hebrew word, וְד֥וֹר. wə·ḏō·wr, instead of the Greek word αἰῶνι, then I can understand how many people have been blinded by the previous traditions which have become entrenched within today's understanding of the scriptures.
By rigidly applying this misunderstanding to Matthew 24:34 our understanding of all of Matthew 24 is skewered and becomes misleading.
Shalom