First we need to make clear what you mean by social hierarchy. Social hierarchy manifests in different ways, the most prominent of which is class, as currently defined by their relationship to the means of the production. There are other aspects (which we call intersectionalities) which don’t necessarily manifest in a hierarchical sense like race, gender, ethnicity, religion, etc. which will become more prevalent once class is eliminated, for sure. (More on this in a bit)

Now recall earlier where I mentioned that communism is an extrapolation of capitalism from feudalism. During the transition to capitalism, the capitalists eliminated the nobility class, by seizing state power. Extrapolating from that, the transition to communism (into socialism) will seek to eliminate the capitalist class by seizing state power. (Which is easier said than done because this is a multiplayer game and you have to defend against imperialists.)

Once we eliminate the capitalist class, what is left? Only the proletariat, as well as intersectionalities and prejudices left over from capitalism and imperialism that we must acknowledge and resolve.

And only once those are resolved, can we reach communism.

So the answer to your question is “bit by bit, starting with the capitalist class.”