Social relationships are important to human well-being and interaction. Recently, there has been growing interest in how they are formed in various digital media, including social media and video games. Amid the rise of digital engagement, the metaverse has emerged as an essential virtual environment for social interaction. Unfortunately, there is limited understanding of how social relationships are developed and maintained within the metaverse. In this study, we explored the dynamics of social relationship development in a metaverse world. Using a one-shot case study, we assessed the roles of immersion and embodiment, as well as the moderating effect of copresence, in building social relationships through multiple regression analysis. Our findings show that with higher levels of immersion and embodiment, the formation of social relationships in the metaverse is significantly improved. Copresence further intensifies these effects, which is indicative of its crucial role in virtual social interactions. These results indicate that enhancing the immersion, embodiment, and copresence elements in metaverse environments can encourage stronger social bonds among users. Overall, this study advances our understanding of online social relationship formation in the metaverse environments and its design and development.