I'm currently learning about orbital hybridization in carbon.
I see that carbon has an electron configuration of 1s2 2s2 2p2.
However, there are actually three p-orbitals in the second shell, namely px, py and pz, which could each hold two electrons. However, there are only two electrons to be distributed on these three orbitals. Which orbitals do they occupy? Since their energy levels are identical, is it random?
I also learned that the three p orbitals can be combined with the 2s orbital (sp3 hybridization) to form four new hybrid orbitals. It then makes sense that the four electrons available each occupy one of the four new orbitals (so that each of them holds one electron), because this way, they can have the greatest spatial distance to each other (I assume they "want" this as they repel each other).
However, how are the second shell electrons distributed in a non-hybridized carbon atom? Does such an atom even naturally occur or does it always hybridize?
Why is this the case, and not, for example, 1s2 2s2 2py1 2pz1?