  It is shown that the initial conditions in the quasi-Heisenberg quantization
scheme can be set at the initial cosmological singularity per se. This
possibility is provided by finiteness of some quantities, namely momentums of
the dynamical variables, at a singularity, in spite of infinity of the
dynamical variables themselves. The uncertainty principle allows avoiding a
necessity to set values of the dynamical variables at singularity, as a wave
packet can be expressed through the finite momentums. Influence of the initial
condition set in the singularity in such a way to a number of gravitons under a
vacuum state, arising during later evolution, is investigated. It is shown
that, even choosing of some special state at the singularity minimizing late
time expansion rate, some amount of gravitons still appear in the late time
evolution.
