SOX is a specific law with the motivation of giving markets more confidence in public stocks (for example must hire external auditors, certain board member rules, how certain assets must be valued, etc).
The SOX audit is to make sure that law is followed.
One criticism of SOX is that encouraged many startups and other businesses to remain private.
So long story short, no. Our government does not resemble a public stock corporation and these things don’t have an analog.