The present study investigates the co-moment between sustainability (STB), Bitcoin (BTC), gold, and carbon emissions (CO2) by analyzing daily data spanning from June 3, 2013, through June 30, 2023. In this study, we employ wavelet connectedness such as wavelet transform coherence (WTC), partial wavelet coherence (PWC), continuous wavelet transforms (CWT), and multiple wavelet coherence (MWC) to examine the interconnections among the variables under investigation. The results demonstrate that, as a sustainability-focused index, STB shows connectedness with CO2 emissions, reflecting the increasing importance of STB considerations in financial markets. Gold, often considered a safe-haven asset, has shown a unique relationship with the other variables, especially during periods of economic uncertainty. As a relatively new and highly volatile asset, BTC exhibits different dynamics than traditional assets like gold. Sustainability considerations have become increasingly important in financial markets, and indices like STB reflect this growing trend. Bitcoin appears to exhibit a stronger and more frequent positive correlation with the broader financial market compared to its correlation with gold. The outcomes of the study are validated through a robustness check of time and frequency connectedness. These findings have significant ramifications for businesses, investors, and legislators who must navigate the complex interplay between STB, money, and environmental dynamics in a constantly changing global context.