A growing number of galaxy clusters at z = 1-2 is being discovered as part of deep optical, IR, X-ray, and Sunyaev-Zel'dovich effect surveys. For a complete picture of cluster formation, however, it is important that we also start probing the much earlier epoch, between redshifts of about 2 and 7, during which these clusters and their galaxies first began to form. We use the Millennium Simulations to track the evolution of dark matter and galaxies in about 3000 clusters from the earliest times to z = 0. We define an effective radius R sub(e) for proto-clusters and characterize their growth in size and mass with cosmic time. This paper provides the general framework that will allow us to extend the study of cluster formation out to much higher redshifts using the large number of proto-clusters that are expected to be discovered in, e.g., the upcoming HETDEX and Hyper Suprime-Cam surveys.