"We have hot soup."
Translation:Nous prenons une soupe chaude.
yeah i did the same thing you did at first... but i guess the context is that the people in the example are consuming the soup, not possessing it. Therefore, we have to use "prendre" to describe them consuming it. I don't know if there's any other way to tell these kinds of things other than just the context they are in.
To be honest, seeing the English translation of the French sentence, it sounds kind of wrong since 'We have hot soup' sounds like you're possessing it, instead of eating it; I think that "We're having a hot soup' would be better, at least for the translation. And regarding your question more, "Nous avons une soupe chaude' would - yes - express possession i.e. you have a hot soup, but you're not necessarily consuming it.