On the basis of the astounding uniformity of background radiation, we can conclude that the universe was very nearly uniform at that stage in its development that it became transparent.
Nevertheless, the universe is currently exceedingly lumpy. All most all the visible mass is tied up in stars, which make up a vanishingly small proportion of the total volume of the universe. Clearly, when it became transparent the universe had just the right lumpiness to seed the accumulation of matter in stars.
As the Big Bang and the Clump both lead to more or less the same state when the universe became transparent, there are no major differences in credibility relative to these paradigms. There is therefore no need for explanation lemmas.