Let me add a little clarification. On rereading the post this addition might be needed.....
The interaction cross section that gives the observed fractional abundance of DM is a constant independent of DM particle mass is more clear.
The key insight is that the fraction of the universe that is in dark matter has different dependencies on the DM particle interaction cross section and mass.
In the Standard Cosmology (inflation) the interaction cross section is fixed and independent of the DM particle mass. So the interaction cross section is fixed and independent of DM particle mass.
But for Big Bounce the observed mass fraction of DM is constrained to lie on a curve in particle mass - cross section such that the observed mass fraction is proportional to the cross section and inversely proportional to the square of the particle mass.In the Big Bounce without inflation the interaction cross section has to decrease as the inverse mass squared. If the DM particle is sufficiently massive its interaction cross section would have to be too small to be detected with terrestrial experiments. (It eventually gets to be below the cosmic neutrino background and undetectable.)
The Inflationary Big Bang curve and Big Bounce curve are easily separated so a lab detection, necessarily involving measuring a cross section and a mass, will falsify one or the other idea. If we are REALLY lucky both can be falsified and we'll have an opportunity to learn something new!