I would be curious at to why you think the Rapture is a secret event. When I look at verses like 1 Thes 4:16-17 it seems literally clear that God will be coming loud with trumpets etc. Is it possible that the “thief in the night” could refer to Christ coming unexpectedly rather than silently?
Believers are to expect the Rapture. We shouldn’t be taken by surprise because the Lord gave us recognizable signs to alert us to the nearness of the End Times. (1 Thes. 5:4) Since the Rapture is an End Times event, when we begin to see the signs He gave us, we should expect the Rapture. I called it a secret event because it isn’t part of an identified series. In other words, once we’ve entered the End Times its occurrence isn’t dependent upon a specific preceding event. It’s exact timing will remain a secret until it actually happens.
I also believe that it’s a number specific event rather than a time specific one. The Church will apparently contain a specific number of believers and when that number is reached the rapture will occur.(Romans 11:25) Since no one knows the number, no one knows the day or hour.
As far as the sounds accompanying it, there are instances in Scripture where only His intended audience hear the sound of His voice. Those left behind after our disappearance may only recall hearing something like thunder. What’s more the event will likely remain an unsolved mystery for some time.
I say this because there will be many who think of themselves as part of the Church but will be left behind. Some of them might even be quite prominent. To admit that the Church is gone and they’re not is to admit that they were never saved, something that will be very difficult.
And for non-believers to admit that the Rapture has occurred will be equally difficult because it will mean that Bible Prophecy has been fulfilled before their eyes an they don’t believe in the Bible.
And finally the one in charge of end times events on Earth will be trying to convince the World that he’s God. He can’t very well admit the the real God took the Church away.
Other reasons will have to be found for our disappearance, reasons that allow the people of Earth to avoid admitting the fact that there is a God, He does intervene in the affairs of man, and He’s doing exactly what He said He’d do.