Synchronization and bursting activity are intrinsic electrophysiological properties of in vivo and in vitro neural networks. During early development, cortical cultures exhibit a wide repertoire of synchronous bursting dynamics whose characterization may help to understand the parameters governing the transition from immature to mature networks. Here we used machine learning techniques to characterize and predict the developing spontaneous activity in mouse cortical neurons on microelectrode arrays (MEAs) during the first three weeks in vitro. Network activity at three stages of early development was defined by 18 electrophysiological features of spikes, bursts, synchrony, and connectivity. The variability of neuronal network activity during early development was investigated by applying k-means and self-organizing map (SOM) clustering analysis to features of bursts and synchrony. These electrophysiological features were predicted at the third week in vitro with high accuracy from those at earlier times using three machine learning models: Multivariate Adaptive Regression Splines, Support Vector Machines, and Random Forest. Our results indicate that initial patterns of electrical activity during the first week in vitro may already predetermine the final development of the neuronal network activity. The methodological approach used here may be applied to explore the biological mechanisms underlying the complex dynamics of spontaneous activity in developing neuronal cultures.