The background radiation they discovered to be a relic or remnant of the big bang, and the universe's expansion as shown by Hubble, were indeed determinative.
Neither of these is "determinative."
Hubble postulated, by analogy, that the red-shift he saw in stellar light was caused by recessional velocity. It seemed like a good idea at the time, since everyone was familiar with the doppler effect, and quickly gained ascendency as the "it explains everything" idea, but at the cost of ignoring actual observations to the contrary, such as
physically entrained objects having radically different red-shifts, or reinterpreting them to fit into a big bang cosmology.
The background radiation argument is simply speculation. The big bang theorists have no mechanism to explain why background radiation should be 2.7K except to say that the temperature is what the radiation left over from the big bang happened to have cooled off to by this much time after the initial big bang, though that amount of time keeps growing and growing. On the other hand,
if all the helium in the universe is formed by fusion of hydrogen atoms in stars and leads to radiation, the temperature of that radiation would be 2.7 K, which is what it happens to be.
“Determinative” as far as the conventional scientific wisdom is concerned. I am perfectly satisfied that the Bible generally, and its numerous creation accounts specifically, which accord with each other, are true. Scientific understanding will continue to evolve, but increasingly it verifies what the Bible has always maintained.