The disciples do not tell us (in that passage of scripture) what you want to know. They seem to have had one thing in mind, but if Jesus had more than one thing in mind, his answer would be the best way of finding that out. After all, many times people asked him questions that he either did not answer as they expected, or he told them a parable that sent them away thinking, in order to find the answer.
In this case, Jesus did not answer with a parable except much further along in the passage, when he could have switched to another (though related) matter. To begin with, he answered directly about signs that would point to the destruction of the temple in Jerusalem. That is the unarguable context from ch. 23 vs. 37 At the start he detailed signs that would NOT mark the end of that particular age - the age of temple worship based in Jerusalem (24:2). I agree that the best meaning is 'age'. The Greek for 'world' is not 'kosmos' but 'ouikomene' which means a localised area or the known inhabited earth at that time.
Jesus began by warning his disciples about being deceived regarding that matter. He foretold the arising of many false prophets, claiming to be the Christ (Messiah). He said not to heed rumours of wars, nor when nation arose against nation, nor when famine, pestilence and earthquakes happened in various places. They could expect that, "but the end is not yet" (vs. 6).
However, as Jesus went on to what would happen by way of signs, it appears he was getting them to think about a global situation that - at that time - they had no idea about. They were only thinking about the nation of Israel. He was directing them to think about the good news (gospel) of Christ being proclaimed world-wide. He foretold a time of tribulation "such as was not since the beginning of the world to this time, no, nor ever shall be. And except those days should be shortened, there should no flesh be saved; but for the elect's sake those days shall be shortened." (vss.21-22)
When the literal temple of Jerusalem was finally destroyed in A.D. 70 and thousands of Jews had died horribly or were taken off as slaves, that would fulfil some of the things Jesus foretold, yet by the time the aged apostle John received the visions of the revelation of Jesus Christ, circa A.D. 95, only then did more significance attach to Jesus' prophecy in Mat. 24. By then, the apostles would have experienced seeing the resurrected Christ and his return to heaven; by the time of the Revelation, they would recognise phrases about the greatest tribulation ever, of the days having to be cut short so that the elect would not be deceived, and Christ's spectacular descent from the clouds down to earth, for the Day of Judgment.
We may be confident that Christians entering the second century would have a greater insight into, and understanding of Jesus' Mat. 24 prophecy than when on that mount, asking Jesus face to face about Jerusalem's destruction. Likewise with ourselves today. We look at all those questions from our point of view, with a far greater grasp of what has happened after Jesus' prophecy. But you ask what the disciples were thinking at that time, long, long ago.
My answer is that they appeared to be thinking about the temple in Jerusalem being destroyed, thinking that would coincide with Jesus returning in triumph as Israel's king. That was the age they were thinking about, one that would end with that destruction. They had a lot to learn (as do we!)