In this work, the suitability of natural raw materials with various modifications of SiO2—granite sawing waste (quartz) and opoka (a mixture of cristobalite, tridymite, quartz, and an amorphous part)—for the 1.13 nm tobermorite and xonotlite synthesis is examined, and their specific surface area, pore diameter and volume, and the predominant pores are determined. Hydrothermal syntheses were carried out at 200 °C for 12 and 72 h from mixtures with a molar ratio of CaO/SiO2 = 1.0. X-ray diffraction analysis, simultaneous thermal analysis, and scanning electronic microscopy were used, which showed that in the lime–calcined opoka mixture the formation of crystalline calcium silicate hydrates takes place much faster than in the lime–granite sawing waste mixture. The high reactivity of amorphous SiO2 results in the rapid formation of 1.13 nm tobermorite and xonotlite (12 h). According to Brunauer, Emmet and Taller (BET) analysis data, this product features a specific surface area of ~68 m2/g, a total pore volume of 245 × 10−3 cm3/g, and has dominating 1–2.5 nm and 5–20 nm diameter pores. This porosity of the material should provide good thermal insulation properties of the products made from it as no air convection occurs in the fine pores.