> Objects with higher temperature have higher entropy
That surely must be a bit too oversimplified, since that would imply that the beginning of the observable universe had more entropy than the current one (given that it was way hotter than the present)
We know that early universe was low entropy - that is the explanation for the 2nd law of thermodynamics. That is known as the past hypothesis. The laws of physics dictate that the most likely state to come from and go to, is higher entropy because there are vastly more high entropy states than low. That directly violates the 2nd law, but is not unreasonable. Imagine 2 boxes of gas with 10 gas molecules in side A and B. They are separated by a wall with a single small hole in it. Every now and then a gas molecule with go from one side to the other, A to B, without one going the other way. We just went from a high entropy state to a lower entropy state in a closed system.
But, coming from a high entropy state does not fit with the world we see, so we're pretty sure that the past hypothesis is true.
One of the leading theories about the early universe and how it lead to the world we know today, is inflation. In that theory "stuff" is basically created out of nothing, meaning that the early universe was small, hot, and with (relatively) few particles in a specific configuration. The inflation and reheating dramatically increased the entropy. In other words - there was much less stuff, and it needed to be in a particular configuration to expand into the universe as we know it. That is low entropy.
Note: I am not a theoretical physicist, so the above is my layman understanding of the topic.
That surely must be a bit too oversimplified, since that would imply that the beginning of the observable universe had more entropy than the current one (given that it was way hotter than the present)