The trampling has already occurred. It’s historical. It’s fact. The Temple to this day does not exist. If the Christians were concerned about the Jews, the Mosques would have been raised, and the Jews brought back to rebuild their Temple during the Crusades. That’s not really what happened.
Readily it is visible that modern gentile Christians have largely acted as an aloof club all to themselves. There are some bright exceptions, but they are mostly denominational, such as Southern Baptist. But I doubt that even Southern Baptists are, of themselves, going to march up to Jerusalem and raze (not raise) Islamic temples -- or that it's reasonable to place this criterion upon them while they are still largely gentile. The third restoration of the Temple is an end times thing and attempts to rush it ahead of schedule would only meet with God's wrath.
But one thing that COULD arise from Southern Baptists (and closely allied congregations like many bible churches) might be an unprecedented evangelization movement to undermine Islam itself. Just to think about that is quite an eager anticipation.
There is a great case to be made to Muslims for Christian faith. Jesus is the prince of peace — Mohammed is forever itching for war, as well as dictating a barbaric standard of community.