From third law of thermodynamics, if temperature $T\to0$, the entropy $S\to0$. In another way we can also say that with the rise of temperature, the entropy will rise.
But we also know that our universe at the very beginning of the time was a very hot dense state of a fire ball and it was in the very low entropy state. So here we observe that temperature $T$ is high but entropy $S$ is low. Is it in the contradiction with the third law of thermodynamics? Or am I explaining/observing it wrong?
Or can we say that we have two system, both in ordered state (low entropy) but one with extremely high temperature (universe at early state) and one with extremely low temperature(Bose Einstein condensate)? How is it possible?