It is proper to accept the Big Bang theory as the most plausible explanation for the origin of the universe?

I think that it's important to remember that peopl have traced back to the beginning of the universe with calculations, and found that we should see a relic radiation field over the whole sky with a temperature of a few degrees Kelvin. Several years later, this was discovered. It is very rare in science for a theory to make such an unusual, specific prediction, and for that prediction to turn out to be correct, without the model that made the prediction being correct. If the Big Bang model were capable only of explaining things which had been seen before the model were developed, then you might have a point, but that's not the case here.