Hey,
You would need to use a slider then.. one that sized based on the image size of your background... which isn't how backgrounds work so that's why a slider or hero script because you would need js to come into play.
Backgrounds don't ever determine size. They are only a background. So you can set the background to "contain" which will make sure the whole image is show but it will mean that the area you placed the background into will have areas with no background image.
I wrote a post here to explain: http://www.kadencethemes.com/background-image-sizing/
Sounds like you're wanting the container to adjust to fit your image but that image you want as a background. So my best advice would be to look for a slider that does this.. Premium theme has a couple options. I'm just not aware of free plugin options although I'm sure there are some free slider plugins that do this.
I hope that helps.
Kadence Themes