The superatomic structure of film-forming sols obtained by the acid hydrolysis of tetraethoxysilane (TEOS) in an aqueous medium (free of organic solvents) was studied using the SAXS method. The formation of nanoparticles (NPs) was confirmed in alcohol-free silica sols with both a low (1 vol. %) content of TEOS and a high (10 vol. %) content of TEOS, hydrolyzed in an aqueous-alcoholic medium. A trimodal size distribution was revealed for the resulting NPs, with radii ranging from less than 1 nm to ~11 nm. The volume fraction of NPs tends to grow with increases in TEOS concentration, as well as with the introduction of magnetic NPs of iron oxides into silica sols. The synthesized silica sols and suspensions based on silica sols with FexOy NPs were used for the pre-sowing treatment of white and cauliflower cabbage seeds in order to provide a functional coating on their surfaces, thereby improving seed germination, stimulating their growth in the early stages of development, and suppressing the effect of phytopathogens. The effect of the pre-sowing seed treatment in sol-gel compositions on seed germination and the growth characteristics of plant seedlings is analyzed, including the influence of iron-oxide magnetic NPs’ compositions and concentrations in silica sols.