Typically, the theory of open quantum systems studies the dynamics of the reduced state (density operator) of the system. However, in the early stages of evolution, it is impossible to separate the reservoir dynamics from the system dynamics. We study the joint dynamics of the system and reservoir at an early stage of evolution and the pre-relaxation of the joint state to a so-called kinetic state. A kinetic state of the system and reservoir is characterized by the fact that it is completely determined by the reduced density operator of the system alone. Only after the formation of a kinetic state, it becomes possible to describe the evolution of the reduced density operator of the system in terms of a semigroup. We rigorously prove the pre-relaxation to a kinetic state for two exactly solvable spin-boson models: the pure dephasing spin-boson and the RWA spin-boson with the zero temperature of the reservoir. The work was inspired by Bogoliubov's ideas about the derivation of the Boltzmann equation from the Hamiltonian dynamics and we will discuss the analogies.