So far I have come to know that changing magnetic field (or flux) creates current, also known as Faraday's law of electromagnetic induction.
This is a mis-statement of Faraday's law of induction. Faraday's law, $\nabla \times \vec E = -\frac{\partial}{\partial t} \vec B$ says that a changing magnetic field creates a curling E field, not a current. That is purely an EM field phenomenon and has nothing whatsoever to do with atoms, the atomic level, or matter.
Matter can respond to that E field, e.g. by Ohm's law, to produce a current. When that happens the explanation will be related to the matter by whatever principle connects the atomic level to the macroscopic constitutive relationship. For conductive materials that will be something like the Drude model or its various refinements. For other materials it will be different.
But regardless of the type or presence of matter, the induction is a field phenomena that must be understood as a field phenomena and not as some atomic thing.