Is there any way to recover a camera view (photo) that I didn't take?
If the picture was not actually taken, you cannot recover it. Your phone doesn't record what's done on the camera screen, unless you actually record a video or take a picture.

If it would be recording the whole time, that would take all your phone's memory and it would probably be against some privacy laws.

The above is assuming that you didn't download a special camera app that has this function.