Steady State Theory is (or was) not the real competitor of the Big Bang Model as Steady State also submits to the notion of ‘Expanding Universe’. In case universe is not expanding then both Big Bang and Steady State theories are equally wrong. Thus if there is competition, that is within single niche. It is not exactly like competition between two different camps. They both operate within a single camp and the actual competing camp has yet to emerge.
The only so-called evidence of the Big Bang Theory is that Georges Lemaître had derived Hubble type redshift-distance relationship in light coming from far off galaxies from relativistic (GR) equations in year 1927 whereas Hubble could experimentally find this relationship in year 1929. In this way, it is claimed that (GR based) mathematics had already successfully predicted that important relationship two years before its actual discovery.
But this so-called evidence of the Big Bang Theory is not acceptable because Georges Lemaître had not derived that relationship from (GR) equations. In year 1927, he had derived that relationship not from GR equations but from a method which he took from Hubble himself.
Georges Lemaître’s 1927 French article remained unnoticed until he, with the help of his former teacher , published English translation of his 1927 article. That English Translation was published in year 1931 i.e. two years after the experimental discovery of redshift-distance relationship.
There was huge blunder in the 1931 translation article. In the original French article, there was whole para under equation No.23 where Lemaître had clearly mentioned that he had data of redshifts of various galaxies and he also took method of finding distance of those galaxies from Hubble. But in the manipulated translation of 1931, this whole para was replaced by a single sentence.
This crucial omission was in the notice of Arthur Eddington and he was guiding Lemaître to present translation in that particular way. Yes, he is the same Arthur Eddington who already had authenticated whole General Relativity through his famous (may be notorious) 1919 experiment of confirming bending of light ray during solar eclipse.
And following is translation of omitted para under eq.23. This translation is given at the end of this paper.
In 1931, the strategy worked and GR equations were projected, through a manipulated translation, as having extraordinary magical powers. But equations had no magical power as such. It was a trick. Arthur Eddington was already expert in those tricks.
For further details please see: A Philosophical Rejection of The Big Bang Theory