Before you start, put the smart guides and snap to point on, disable snap to grid in the view menu.
See the cartoon and the explanations below:
1) Have 3 identical rectangles and your mountains, nothing is grouped! The rectangles have temporarily black strokes only to make them visible in this image (=1)
2) Drag your objects to their final places. Goto object > Arrange to send objects to bottom or bring them to front. The 3 lowermost in the stack must be the rectangles. The ordering is possible also in the layers panel, which you seem to have got visible in your screenshot.
3) Select the topmost rectangle. Bring it to front. Select with holding shift also the small mountain.
4) Goto Object > Clipping Mask > Make. The foreground rectangle vanishes and the mountain gets clipped. The clipping result pops automatically to foreground, but it will be fixed when you clip the other mountain, which will pop to foreground.
5) Bring again a rectangle to front. Select it and the rightmost mountain.
6) Goto Object > Clipping Mask > Make. The second mountain gets clipped and only one rectangle is left at the background.
You can release the clipping masks as long as you have not expanded nor rasterized the clipped shape
Seeing as you tagged clipping mask in your post I assumed you knew how it worked, hence my comments.
You do not need to give the mountains the exact same border radius in the exact same place as the border of the rectangle, that would indeed be very tedious. You can simply clip the shapes together.
Adobe has an excellent video tutorial on how to do that: https://helpx.adobe.com/illustrator/using/clipping-masks.html