If this big bang as exploding firework model is to have any validity, it needs to explain a couple of things.
•Why don't we see a central void? When something explodes, the debris cloud starts out spherical, but after a little time has passed, you always get an expanding shell of material around a central void, rather like a planetary nebula. If the universe contains such a void, it should be pretty easy to find.
•Why isn't there a large difference in the apparent size of galaxies, at the same redshift, on different sides of the sky? On this side of the explosion, everything is moving in the same outward direction as us, but the redshift for galaxies on the opposite side of the explosion would be due to the sum of our outward velocity, and the outward velocity of the distant galaxies. Without some serious kludgery, that'd require the redshift vs distance equation to be highly assymetric. AFAIK, it's not.