In this contribution, we present the preparation and structural characterization of a new type of alternative (sodium silicate-free) geopolymer system. A new procedure of geopolymer synthesis based on the preparation of a reactive geopolymer precursor by direct calcinations of low-quality kaolin with Na/K hydroxides is introduced. The subsequent formation of geopolymer matrix does not require activation by alkaline silicate solution. The compact and hardened material was prepared only by adding a small amount of water. Besides the introduction of a new synthetic procedure, we focused also on the systematic study of chemical structure, mineralogical composition and hydrothermal stability of the prepared geopolymer systems as seen by solid-state NMR spectroscopy and powder X-ray diffraction (XRD). An important part of our contribution is the demonstration of structural and mineralogical changes induced by hydrothermal treatment and long-term aging of the prepared geopolymers. It was found that redistribution of basic structural units (SiO44- and AlO45-) and gradual formation of zeolite fractions can be related to the observed changes in mechanical properties. Up to a certain level, the presence of zeolites enhances the mechanical properties of the prepared geopolymer systems. However, the additional formation of a new generation of zeolite fractions, occurring over the long-term period causes an inversion of this trend and a dramatic reduction of mechanical strength. Nevertheless, formation of the geopolymer matrix by alkaline and thermal activation of low-quality kaolin has the potential to be used in ecological problems solving (solidification of powdered and dangerous waste materials).