At the Big Bang, when everything was close together, why did it not "collide", violating Planck length or Pauli Exclusion Principle? How could so much matter, or &quot;all&quot; in fact, have been concentrated in a smaller universe without being in the actual same place? Why did this not result in undercutting the Planck Length or violating the Pauli exclusion principle?
The Pauli Exclusion Principle forbids two indistinguishable fermions occupying the same quantum state. It does not prevent them getting arbitrarily close together so long as they have very different momentum states.
The big bang model relies on classical General Relativity. When we go back to scales where quantisation of space might become important (i.e. Planck length scales, corresponding to the first $\sim 10^{-43}$ s of the universe) then GR needs to be replaced by some quantum theory of gravity (which we don't have).