Online Social Networks (OSNs) are a cornerstone in modern society, serving as platforms for diverse content consumption by millions of users each day. However, the challenge of ensuring the accuracy of information shared on these platforms remains significant, especially with the widespread dissemination of disinformation. Social bots -- automated accounts designed to mimic human behavior, frequently spreading misinformation -- represent one of the critical problems of OSNs. The advent of Large Language Models (LLMs) has further complicated bot behaviors, making detection increasingly difficult. This paper presents BotHash, an innovative, training-free approach to social bot detection. BotHash leverages a simplified user representation that enables approximate nearest-neighbor search to detect bots, avoiding the complexities of Deep-Learning model training and large dataset creation. We demonstrate that BotHash effectively differentiates between human and bot accounts, even when state-of-the-art LLMs are employed to generate posts' content. BotHash offers several advantages over existing methods, including its independence from a training phase, robust performance with minimal ground-truth data, and early detection capabilities, showing promising results across various datasets.