In summary, we have developed a fully data-driven system identification framework capable of organizing and utilizing disorganized datasets. We collected data from oscillating agents, initially without any knowledge of an optimal ordering, and successfully discovered an emergent space. Additionally, we reordered time, which was purposefully shuffled, and organized trajectories originating from systems with different coupling strengths, K. In this process, we generated labels (emergent embeddings) from our unlabelled dataset via unsupervised learning. Furthermore, we used these newfound labels to construct a generative model (DeepONet) that incorporates our emergent space and time embeddings along with the parameter coupling strength embedding, enabling accurate predictions even for out-ofdistribution (OOD) samples.