Landau writes "It is found, however, that a frame of reference can always be chosen in which space is homogeneous and isotropic and time is homogeneous."
Does he mean that we can prove the existence of an inertial frame or does he want to say that it is assumed by doing enough number of experiments?
Can we start with some axioms and definitions of properties of space and time and then deduce the existence of such a frame in which space is homogeneous and isotropic and time is homogeneous?
The edition Mechanics was 1st published at 1960 and was written earlier than that.
Landau died in 1968 aged 60.
Just 4 years before, in 1964, the CMB was discovered and the properties of it was unknown for years after.
It appears that Landau's saying was vindicated with a referential with the properties of the CMB.
The Earth (we, and the labs) is moving in relation to the CMB and the universe appear to us to be non isotropic. From the perspective of CMB, the referential of light, i.e. where light propagates equally in all directions, the universe is isotropic.
In addition every observer in the universe can use (share) a common length and time base using the CMB properties for the calibration purposes.
This special referential is not attached to any observer as with the Einstein ones.
