As Artificial Intelligence (AI) becomes increasingly integrated into our lives, the need for new norms is urgent. However, AI evolves at a much faster pace than the characteristic time of norm formation, posing an unprecedented challenge to our societies. This paper examines possible criticalities of the processes of norm formation surrounding AI. Thus, it focuses on how new norms can be established, rather than on what these norms should be. It distinguishes different scenarios based on the centralisation or decentralisation of the norm formation process, analysing the cases where new norms are shaped by formal authorities, informal institutions, or emerge spontaneously in a bottom-up fashion. On the latter point, the paper reports a conversation with ChatGPT in which the LLM discusses some of the emerging norms it has observed. Far from seeking exhaustiveness, this article aims to offer readers interpretive tools to understand society's response to the growing pervasiveness of AI. An outlook on how AI could influence the formation of future social norms emphasises the importance for open societies to anchor their formal deliberation process in an open, inclusive, and transparent public discourse.