Application of the Theory of General Relativity to the large-scale structure of the Universe leads to various cosmological theories. Of these, the most important are a class of solutions called Friedmann cosmologies that lead to what is termed the hot big bang. The starting point for these theories is what is termed cosmological principle:
This clearly is not true on short distance scales: your classroom probably looks rather different from your dormitory room, and we certainly see distinguishing structure like galactic superclusters and the Great Wall up to at least 100-200 Mpc scales. However, well beyond those distance scales there is strong observational evidence for the cosmological principle.