The transition from single-cell to multicellular behavior is important in early development but rarely studied. The starvation-induced aggregation of the social amoeba Dictyostelium discoideum into a multicellular slug is known to result from single-cell chemotaxis towards emitted pulses of cyclic adenosine monophosphate (cAMP). However, how exactly do transient short-range chemical gradients lead to coherent collective movement at a macroscopic scale? Here, we use a multiscale model verified by quantitative microscopy to describe wide-ranging behaviors from chemotaxis and excitability of individual cells to aggregation of thousands of cells. To better understand the mechanism of long-range cell-cell communication and hence aggregation, we analyze cell-cell correlations, showing evidence for self-organization at the onset of aggregation (as opposed to following a leader cell). Surprisingly, cell collectives, despite their finite size, show features of criticality known from phase transitions in physical systems. Application of external cAMP perturbations in our simulations near the sensitive critical point allows steering cells into early aggregation and towards certain locations but not once an aggregation center has been chosen.