Space is indeed infinite, but there is no observable space before the explosion, so in a sense, there is no space before the explosion.
Of course, the big bang theory is still controversial, and I can't explain it. Anyway, The Big Bang Theory as a whole has no fatal flaws.
And the explosion is not the original fireball, but a gravitational singularity.
The gravitational singularity, also known as the singularity of time and space, is a "point" mentioned in the Big Bang cosmology, that is, the starting point of the Big Bang. According to this theory, the universe (space-time) was formed after the "big bang" of this "point". Singularity is a "point" with infinite density, infinite curvature of space-time height, infinite heat and infinitesimal volume, and all known physical laws fail at singularity.
The two most important spatiotemporal singularities are curvature singularity and cone singularity. Singularities can usually be distinguished by whether they are covered by events or not. According to the general theory of relativity, the initial state of the universe before the Big Bang was a singularity or a single point. Another kind of singularity predicted by general relativity is inside a black hole: any star that collapses toward the center will form a black hole, and a singularity covered by the event world will be formed inside it, causing all matter to flow to a point (if the black hole is rotating, it is a spiral). These singularities are curvature singularities.