Physical proof is simply the experimental proof. The redshifts that scientists have observed in light coming from far off galaxies are NOT due to Doppler’s effect thus do not amount to physical proof. That is a different kind of redshift which is called Cosmological Redshift.
This redshift is not proof of receding of anything. The only proof which Big Bang supporters have is a mathematical proof (FLRW metric). Its meaning is that the theory (Big Bang) is NOT developed out of experimental findings. It is NOT developed out of Doppler’s Effect. It is developed out of FLRW metric which only ‘explains’ or ‘attempts to explain’ the observed fact of ‘cosmological redshift’. Likewise, theory is also not developed out of experimental finding of CMBR. Only thing is that experimental finding has been ‘explained’ in terms of FLRW metric. At the most they got ‘prediction’ of CMBR from FLRW metric. In this way the maximum thing is that the Big Bang Theory becomes mathematical explanation of CMBR. But after all theory was not developed out of experimental finding of CMBR. At the foundation level, there is only mathematics. Observed facts are only at ‘interpretation’ level. It is possible to interpret both cosmological redshift as well as CMBR in some other way.