We perform a set of large numerical simulations using GADGET2 to study the formation of the first virialized structures and the evolution of their spatial clustering and large scale dynamics in the framework of non-Gaussian CDM cosmological models. Previous works have shown that non negligible deviations from the Gaussian statistics, predicted by a number of inflationary models, can affect the large scale structure of the universe, the statistics of galaxy clustering and the cosmic velocity fields. The recent analysis of the temperature fluctuations in the cosmic microwave background observed by the WMAP satellite have set significant constraints to the level of non-Gaussianity, that, however, should be large enough to delay or anticipate the formation of the first objects in their universe, hence affecting the statistics of the highest peaks in the cosmic density fields associated to the largest virialized structures. The aim of our numerical experiments is to study these processes in detail and to indicate the best observational tests for detecting the signatures of primordial deviations from Gaussianity in the observable universe.