In article ,
Nicolaas Vroom writes:

As far as I understand the fluctuations in the CMB we see to day are
caused by matter fluctuations of the Universe 300000 years after the BB.

Right.

To be more specific in the outer layer of the Universe.

Relative to us.

(It is not the CMB that caused these fluctuations)

Right; the anisotropies in the CMB are due to the fluctuations.

We know the magnitude of the fluctuations of baryonic matter, since that
is what we see. If there were no dark matter, there would not have been
time for these to have evolved to the structures we see today. The idea
is that dark matter can collapse sooner, since it is not stopped by
radiation pressure. The baryonic matter then falls into the dark-matter
potential wells.

During that period apperently there was already a division between
baryonic versus non-baryonic matter which we can observe in the second and
third peak CMB power spectrum. See:
https://en.wikipedia.org/wiki/Cosmic...ary_anisotropy

Right.

The question is how exactly do we know that these peaks are caused
by baryonic and non baryonic matter, of which the last physical is an almost
bare landscape.

I'm not sure what the last clause means. How do we know? Calculate the
power spectrum for various amounts of baryonic and non-baryonic matter
and compare to observations.