Problems understanding naturalistically the beginning of the universe

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... in order to consider if actually the atheist cosmology is plausible ...

What you're asking about is scientific cosmology.  I assume that many Christians accept this cosmology.  And I also assume that many atheists don't.

... since the universe actually began, where did it begin from?

I don't know whether it began: 

• Asimov said it began at the big bang, but then he immediately hedged by saying something like, "Or at least we can _call_ that the beginning, since we don't know what happened before that." 
  
• Hawking made the same move in _A Brief History of Time_.
  
• I went onto campus to find a cosmologist to put this question to.  When I found one, he said, "Nobody knows what happened before the big bang.  Nobody knows what happened before the big bang.  Nobody knows what happened before the big bang."    
  

So I'm not in a position to have an opinion on whether the universe really began, at the big bang or otherwise.

To ask where the big bang "came from" is the same as saying that the universe didn't really begin then.  

In any case, if you can't explain where your gods came from, then you're in no position look down on those who can't explain where the rest of the universe came from.  

The universe is all we know for sure (and sometimes not even for sure), but how can something exist outside the universe? Where was this very hot, small and dense structure since the universe "didn't happen" yet?

If you can't answer those questions about your gods, then you shouldn't feel any better than the rest of us.  

If you want to smugly challenge people to answer a question, it should be a question you can answer yourself.   

Saying, "You people can't answer this question any better than I can," doesn't make you superior.  

Thank you, and I remind that I would want this thread to remain naturalistic, without interference from any kind of religion account.

Your whole point is that religion provides better answers.  You can't prove that without religion.  You can't prove it at all, but you can't even try to prove it without religion.  

Imagine this conversation:

Christian: "My car is better than yours, because your car is an ugly brown."

Atheist: "Oh, yeah?  Well your car is an ugly brown too."

Christian: "I remind you that this discussion is to remain about your car, without interference from any kind of mention of my car."  

In order for your argument to weigh more than zero on the scales of persuasion, you have to show that theists have a better cosmology than scientists.  You can't do that while leaving religion out of it.  


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