The time dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron--electron interactions on the time-dependent charge cumulants, first-passage time distributions and n-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade-

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... Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single electron transfer events.