A further development of the evolutionary picture of A+A collisions, which we call the integrated HydroKinetic Model (iHKM), is proposed. The model comprises a generator of the initial state GLISSANDO, pre-thermal dynamics of A+A collisions leading to thermalization, subsequent relativistic viscous hydrodynamic expansion of quark-gluon and hadron medium (vHLLE), its particlization, and finally hadronic cascade ultrarelativistic QMD. We calculate mid-rapidity charged-particle multiplicities, pion, kaon, and antiproton spectra, charged-particle elliptic flows, and pion interferometry radii for Pb+Pb collisions at the energies available at the CERN Large Hadron Collider, $sqrt{s} = 2.76$ TeV, at different centralities. We find that the best description of the experimental data is reached when the initial states are attributed to the very small initial time 0.1 fm/c, the pre-thermal stage (thermalization process) lasts at least until 1 fm/c, and the shear viscosity at the hydrodynamic stage of the matter evolution has its minimal value, $eta/s = frac{1}{4pi}$. At the same time it is observed that the various momentum anisotropies of the initial states, different initial and relaxation times, as well as even a treatment of the pre-thermal stage within just viscous or ideal hydrodynamic approach, leads sometimes to worse but nevertheless similar results, if the normalization of maximal initial energy density in most central events is adjusted to reproduce the final hadron multiplicity in each scenario. This can explain a good enough data description in numerous variants of hybrid models without a prethermal stage when the initial energy densities are defined up to a common factor.
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