Supplementary Material

- A brief chemistry of the initial part, based on the analysis of the chemical environments; - additional figures about: one small persistent diamond precursor in Sim. VN1; the evolution of the populations of the CDPs; the evolution of the percentage of total H, N and O atoms involved in carbonless molecules; the evolution of the percentage of total C, H, N and O atoms involved in carbon-containing molecules; the raw evolution of the average size of the pure-carbon structures in the foam, the growth/coalescence model and the adjusted parameters for each simulation.