Make a hidden object appear at the press of a button

There are multiple ways to do so. Do not use a mask (word used for your 'white box'. There are easier ways, and you would need to use advanced actions and effects, bit more advanced. 

It is not clear to me yet what you exactly want to do (terminology!):

• You have 3 images which are not in the same location but arranged next to each other.
• You want to have those 3 images to appear on clicking an interactive object, probably a button (don't know why you call it a cover? Is that the mask?).
• Do you want to start with an empty slide, and have the images appear one after other by clicking something?
• Not clear: do you want to replace an original image, or to add the next image and keep the original image? I suspect so because of your description of the 'mask' ?

After your answers, I have 3 possible workflows in mind:

1. Using the timeline to have the images appear automatically one by one. Has the advantage of the ability to add some motion effects. You could add pausing points to need clicks, but it can be completely automatic. You'll learn about using the Timeline in that case. When returning to the slide everything will work as the first time.
2. Using Show and Hide (if necessary) but that is a bit old workflow and has the disadvantage that you'll need to reset the slide if you want to return to it. Not my choice, although Show and Hide sounds familiar to you.
3. Using a multistate object, where in each new state you add or replace an image depending on your answers. Has the same advantage as 1 for resetting, but you cannot add motion effects. I would prefer this workflow in your case. You'll learn about Multistate objects which are one of the biggest timesavers introduced two versions ago.

It appears you may need to look up some YouTube videos about the Captivate timeline and how it works. Objects placed on the slide will appear during playback according to where they are positioned on the timeline.

If you just want a graphic of a cow and a graphic of a boy appear at a certain point in the timeline then you can just drag the starting point of each object to the point in the timeline where you want it to appear.  In the Timing tab, set the Fade In to 0.5 seconds so that the image appears slowly, not suddenly.

Using Adobe captivate