After a surge in popularity of supervised Deep Learning, the desire to reduce the dependence on curated, labelled data sets and to leverage the vast quantities of unlabelled data available recently triggered renewed interest in unsupervised learning algorithms. Despite a significantly improved performance due to approaches such as the identification of disentangled latent representations, contrastive learning, and clustering optimisations, the performance of unsupervised machine learning still falls short of its hypothesised potential. Machine learning has previously taken inspiration from neuroscience and cognitive science with great success. However, this has mostly been based on adult learners with access to labels and a vast amount of prior knowledge. In order to push unsupervised machine learning forward, we argue that developmental science of infant cognition might hold the key to unlocking the next generation of unsupervised learning approaches. Conceptually, human infant learning is the closest biological parallel to artificial unsupervised learning, as infants too must learn useful representations from unlabelled data. In contrast to machine learning, these new representations are learned rapidly and from relatively few examples. Moreover, infants learn robust representations that can be used flexibly and efficiently in a number of different tasks and contexts. We identify five crucial factors enabling infants' quality and speed of learning, assess the extent to which these have already been exploited in machine learning, and propose how further adoption of these factors can give rise to previously unseen performance levels in unsupervised learning.