The evolution of morality presents a puzzle: natural selection should favor self-interest, yet humans developed moral systems promoting altruism. Traditional approaches must abstract away cognitive processes, leaving open how cognitive factors shape moral evolution. We introduce an LLM-based agent simulation framework that brings cognitive realism to this question: agents with varying moral dispositions perceive, remember, reason, and decide in a simulated prehistoric hunter-gatherer society. This enables us to manipulate factors that traditional models cannot represent—such as moral type observability and communication bandwidth—and to discover emergent cognitive mechanisms from agent interactions. Across 20 runs spanning four settings, we find that cooperation and mutual help are the central drivers of survival, with universal and reciprocal morality exhibiting the most stable evolutionary outcomes while selfishness is strongly disfavoured. We also observe two central mechanisms that emerge from cognition, including a cost of moral judgment and a self-purging effect among selfish agents. We validate robustness across multiple LLM backbones, architecture ablations, and prompt sensitivity analyses. This work establishes LLM-based simulation as a powerful new paradigm to complement traditional research in evolutionary biology and anthropology, opening new avenues for investigating the complexities of moral and social evolution.