You don't have to prove something that doesn't exist. Find the evidence, and prove it does.
This evidence is found everywhere. But it's dateable, and you can find the oldest instances of it in the fertile crescent.
You cannot prove it didn’t happen, and I also don’t think it was that likely. Both can be true.
We can't prove that there wasn't some isolated genius who engaged in animal husbandry in Africa before everyone else but was ignored by the rest of his tribe or whatever. But we have managed to place some fairly low upper bound on how much of that could have been happening. At some point it is reasonable to conclude that your typical society in that time and place didn't have access to it.
Edit: clarified the question
Which is to say that no, a very slim chance is not a reasonable position to take in most contexts.
"They’ve successfully analyzed the DNA of two naturally mummified livestock herders who died roughly 7,000 years ago in present-day Libya, which was part of what’s known as the “green Sahara.”
The article says they were practising animal husbandry - I'm guessing they have evidence for that!
So the question is not whether they did it, but whether they started doing it themselves or were taught it by others.
The surprising news is that the spread of animal husbandry didn't seem to accompany the spread of human genes -- the subsistence strategy was adopted by learning, not by people moving.
I don't think this is very shocking because the same thing seems to have happened elsewhere. While agriculture mostly spread by people moving, the culture that developed into all the pastoral cultures of the Eurasian steppe seem to have been hunter-gatherers living in close proximity to farmers.