I stand by my decision.
3/4 of the post is speculation about who could be at fault for the chemical weapon incident in Syria. But the question explicitly says:
If it would be proven that a chemical attack was indeed launched by the Syrian government, what could the United Nations do?
The question is explicitly about the hypothesis that the Syrian government is found to be responsible. So any answer not based on this premise is off-topic.
But not only is this not what the question is about, it's also not what we are doing on this website. Politics.SE is a Q&A site, not a discussion forum. We give factual information and back it up with credible sources. We do not exchange our personal estimations and opinons.
The one quarter of the post which does address the question isn't really an answer either.
The chemical reside, the remains of the ordinance, and the debris of the area of attack need to be independently examined to assert exactly what happened. Supposedly the UN has the capacity to perform such an analysis. However, if they have mandate to demand such authority is questionable, and even if they did the logistics of doing such is extraordinarily difficult and dangerous.
OK, it needs to be analyzed. And then? What are the options the UN can take? How realistic is it politically that they will pass? You say they "don't have mandate to demand such authority"? What international treaties regulate what kind of "mandate" the UN has and what do they say? What does precedent cases from recent history say?
The question already got 5 answers which answer all these points really well. Undeleting this answer with the unnecessary parts removed would not add any useful content.