  Ignorance of the initial condition for the axion dynamics in the early
Universe has led us to consider an $O(1)$ valued initial amplitude, and that
prefers the decay constant, $F_a$, of the QCD axion to be an intermediate scale
such as $10^{12}$ GeV in order to explain the dark matter abundance. We explore
a cosmological scenario of $F_a$ being much larger than $10^{12}$ GeV by
considering the axion and moduli dynamics during inflation to set the initial
amplitude. We show that if the volume moduli (radion) of the extra-dimension is
stabilized mainly by the QCD contribution to the moduli potential during
inflation, the QCD axion with the string-scale decay constant obtains a mass
around the inflationary Hubble parameter. This means that the axion rolls down
to the $\theta = 0$ minimum during the inflation realizing almost vanishing
initial amplitude, and the inflationary quantum fluctuation can be the dominant
source of the current number density of axions. We find natural parameter
regions where the axion explains the cold dark matter of the Universe, while
the constraint on the isocurvature perturbation is avoided. The presence of the
axion miniclusters or axion stars are predicted in a wide range of parameters,
including the one explains the Subaru-HCS microlensing event.
