People in huts eventually band together into villages, villages start to trade goods with one another. Eventually the largest village is able to coerce (either using the threat of force via superior military or through infiltration, bribery subversion etc) the smaller villages into giving it the best deals.
The largest village gets very rich while extracting all the resources and goods from the smaller villages around it. The largest village is able to ram through treaties, trade pacts etc that favor it's interests, it is able to interfere in politics of surrounding villages and sometimes provides backing to despots or outright overthrow leadership of smaller villages that might be doing something the largest village does not agree with.
What you say is true, but when people usually talk about inequality, they're talking about inequality in a specific country. In your example that would be inequality inside a single village rather than between the villages.
Also, with similarly bad faith you could say that when the first group was building their huts, the second group was sharpening their sticks. Once the huts were completed they used their sharpened sticks to coerce the richer people (those with huts) to give them huts too.
The largest village gets very rich while extracting all the resources and goods from the smaller villages around it. The largest village is able to ram through treaties, trade pacts etc that favor it's interests, it is able to interfere in politics of surrounding villages and sometimes provides backing to despots or outright overthrow leadership of smaller villages that might be doing something the largest village does not agree with.