I don't think it's just proof, but actual intent. For most "murder", you need to prove the person intended to kill the other person. You can prove this in many ways, but the key is you have facts that show the person intended to kill another.
In my state, we have a 2nd degree murder statute that also includes what is known as "abandoned heart" murder. That is the type Minnesota charges as 3rd degree murder. How those differ from what most think of as "murder" is that intent can be presumed if someone does something inherently dangerous without a good reason (aka depraved mind) that results in the death of another, he can be guilty. An example is something like shooting a firearm at an occupied residence. A person might not have intended to kill anyone inside, but if someone dies from the shooting, it will be charged as murder.
Did the officer intend to kill George Floyd that day?
I am appalled at the actions taken and am very glad all officers directly involved were fired immediately. I am also glad a murder charge is pending. But, if I were on the jury, without more, I would not find he intended to kill him. I agree if they solely charged him with murder 1 he might very well skate. What I disagree with is that his act should be overcharged because people are (rightfully) enraged. Fuck that.