While Thayer's Lexicon defines Matthew 24:34's usage of genea to mean "the whole multitude of men living at the same time", I'm not really sure where you are getting genea to mean age as in "a thousand years", since Thayer's Lexicon defines genea as age to mean " an age (i. e. the time ordinarily occupied by each successive generation), the space of from 30 to 33 years "
An argument based on the lack of understanding that there are time periods that span periods of time where the end point/vanishing point of that time period is beyond man's ability to comprehend.
In Daniel 7:11-12 we are told that the beasts would be keep alive for a season and a little while period.
In the Book of Revelation 20:1-3 we are told that the season is for 1,000 years and that the little while period of a short duration would follow, nominally 24 years duration, at the end of which the beast(s), the Little Horn/False Prophet and Satan would be captured and dispatched into the Lake of fire and the final judgement of mankind would follow.
In Genesis 15:16a, God told Abraham that in/during the fourth generation that some of his descendants would return to the land of Canaan once again in their own strength, and in the second half of that verse, God also told us that the iniquities of the Amorite people would have not yet reached its conclusion/completion.
Now it was not until 1948 that we saw some of Abraham's descendants return to occupy the land of Canaan to claim it as their own land and to establish a nation upon that area of land.
Prior to 1948 many theologians could not comprehend that God was speaking of a 4,000-year period between the birth of Isaac and some of Abraham's descendants returning to the land of Canaan. Since Isaac was born at the beginning of the third age of mankind in the year 2,049 after the creation of Adam which translates to the beginning of the year 2052 BC. Now when we consider the time span between the year 2052 BC and 2048 AD, we discover that there was exactly 4,000 years between Isaac's birth and the establishment of the nation of Israel in 1948.
Now from 1948 AD until the end of the sixth age of mankind and also the end of the fourth age of the existence of the people group known as Israelites there will be a further 96 years until God removes the beasts of the fields from the face of the earth so that there will be a period of peace on the earth during the 1,000 years of the great Summer Harvest of Souls before the Bottomless pit will be opened to release Satan, the Beast(s) and the Little Horn/false prophet to bring in the period of time which is called the great Tribulation during the little while period of time. At the end of this little period of time we will see Isiah 24:23 and Matthew 24:29-31 unfold when Christ will come in the clouds to begin judging the people groups of the earth.
Matther 24:32-35: - The Parable of the Fig Tree
Matther 24:32-35: - The Parable of the Fig Tree
32 “Now learn this parable from the fig tree: When its branch has already become tender and puts forth leaves, you know that summer is near. 33 So you also, when you see all these things, know that it is near—at the doors! 34 Assuredly, I say to you, this generation/age will by no means pass away till all these things take place. 35 Heaven and earth will pass away, but My words will by no means pass away.
Now in the above quoted scriptures Jesus refers to the "Generation" that will see the completion of all that He has said will happen before His coming, and that that descendant generation will not pass away, is one manner of that these verses could be understood.
Also, the use of the word Genea in the Matthew account could just as easily have been referring to the whole time period of the Seventh Age of mankind.
Either way, what Jesus spoke about in Matthew 24 will occur over a period of 1,024 years from the time that we see the kings of the earth gathering at the place know as Armageddon to put the nation of Israel in her place for wanting to rebuild the destroyed temple until we see Jesus coming in the Clouds will happen as Jesus has said it will.
The seventh age/generation of mankind will have a time span of 1,024 years, just like the six ages/generation before it has had.
Shalom