96% of human vs monkey DNA similarly is not a lot, because most of that DNA is shared throughout all of the animal kingdom. Since human DNA is close to a billion codons long, the remaining 4% is still tens of millions of codons.

COVID-19 is ~30,000 base pairs long (10,000) codons. The 4% difference is 400 codons. That's not a lot. There are many singular proteins longer than that.

Is that proof? No, the same way gravity is just a theory.