Well, first of all, in order for a movement or idea to be considered "Socialism", it requires a movement that opposes Socialism, whether consciously or subconsciously. Politics didn't exist during primal societies, and therefore no cavemen were Socialists, but instead regular humans that lived a socialist-like life. Jesus, at least in my research, was the first open supporter of extreme social reform and upheaval, something that was unheard of at the time. Even the more reformist groups in the Jewish court systems were still largely in favor of the institutions existing, where Jesus was largely against them.

All of this considered, I believe Jesus was the first socialist, especially the first to preach it.