How to synchorize a click with audio in a slide with hotspots?

Yes it is possible, but it's not all that simple.

You need a separate variable to track the fact that each hot spot has been clicked and you need the Hotspots to execute Conditional Advanced Actions that not only execute the action to play the relevant audio file, but also then look at whether or not all of the other hotspots have also been clicked before then showing the button that was previously hidden.  AND...since you appear to only want that button to appear AFTER the audio file has played, you also need to make use of the Delay Next Action By action to time the SHOW action for that button so that it only appears AFTER the correct number of seconds.