Several varieties of virus-like microfossils, morphologically similar to modern giant viruses of the Mimiviridae family, have been identified in microquartzites in the 1.64 Ga volcanogenic-sedimentary strata in Hogland Island in the Gulf of Finland, Russia. Microquartzites contain graphite enriched in a light carbon isotope 12С, as is typical for the rocks forming with participation of living matter. Abundant remains of silificated and ferruginizated microfossils of planktonic microorganisms and virus-like structures were found in fragments of silificated biofilms. However, virus-like microfossils exceed modern giant viruses in linear dimensions by a factor of a thousand or more (Belyaev, 2018; 2019; Belyaev, Yukhalin, 2021) and contain structures similar to eukaryotic nuclei. In addition, data were obtained that can be interpreted as a fact of parasitic relationships of virus-like formations with microfossils of amoeba-like microorganisms. Inside, and in the immediate surroundings of some virus-like structures, small oval zonal formations occur, which, possibly, represent silificated viral particles, the most ancient obligate super parasites similar to "satellite" virophages in mimiviruses (La Scola, et al., 2008). Apatite grains found in the mineralized cytoplasm and nuclei of virus-like microfossils, most likely, crystallized from phosphoric acid residues of decayed nucleotides. This allowed for the first time to roughly estimate the size of the genomes of the most ancient virus-like structures, which exceeded the genomes of modern giant viruses and unicellular organisms by a factor of thousands (Belyaev, Yukhalin, 2021). The genome masses of eukaryotic microfossils and virus-like structures were also estimated following the principle of genomic-nuclear proportionality, according to which the molecular weights of genomes are directly proportional to the size of the nuclei. In this case, the size of genomes of virus-like structures estimated both form the enclosed apatite grains and the size of nuclei, averaged tens of thousands of picograms and, thus, could contain tens of thousands billions of base pairs. It is assumed that microfossils of virus-like structures from the group of unclear systematic position Dinoviridae Incertae sedis were representatives of the extinct family of unicellular facultative parasites or were the ancestors of giant viruses of the Mimiviridae family.