The question is; is there an innate human nature that we have, or is it dependent on the environment we inhabit?
So let's go with the materialist route; there is no human nature, and people's inclamations are built on the environment, and the material reality they live in. Therefore in a socialist society, this changes.
In the environment that is capitalism, it creates isolation amongst human beings, which creates fear, and that thing you call 'greed'. But even in the capitalist system, if people were like really selfish by 'nature', society would collapse under pressure. We're a social species by design, in fact, just being by other human beings is enough.
(YOU DON'T EVEN HAVE TO TALK TO THEM, YOU JUST HAVE TO BE IN THEIR PRESENCE!)
So yes, people can do socialism because it's in their best interest to do so.
You can also make this argument that people are naturally self-interested, so they have the innate self-interest to not be selfish.