The Big Bang model is the current large-scale accepted and tested theory. However, several new physics models or theories propose that there could be a previous Universe. To what extent can be test this hypothesis? I mean: are the CMB polarizations and other fingerprints like the likely cosmic neutrino background or the gravitational waves from the beginning of the Universe the only tests of pre-Big Bang theories? P.S.: I know this question is highly speculative.
Cmb and all other methods you mentioned above are not for discovering pre big bang physics at all. They are for understanding the event of the big bang, so... post big bang not pre. Unfortunately there are no known ways (not even theoretical) to test whether or not another universe preceded our own. Besides I seriously doubt there would be any detectable remnants of that universe and how would we distinguish what was from ours and what was from the other hypothetical universe.