The antibiotic properties of certain things (mould growing on leather, dirt from certain locations, mouldy bread etc.) were recognised quite frequently in many places, and used in medicine. The problem with scaling these up is that actually getting primitive antibiotics to work depends on too many factors outside the users' control. A mineral remedy can be traded, a medicinal plant cultivated with fairly basic technologies. But without a means of identifying specific fungal cultures, cultivating them is hard. People mostly depended on cultures that emerged naturally in certain locations, but these rarely travelled well. I wonder whether the Nubian recipe would have, but I doubt it.
What might have helped is a more empirical approach to medicine. After all, many people in many parts of the world knew that certain moulds and yeasts helped against inflammation. They wouldn't know why (you can't have a correct theory of antibiotics without a theory of infection), but to the empiricist, that does not matter. The evidence would suggest further research into moulds is warranted. Instead, the individual instances tended to be dismissed as superstitious nonsense because the theory didn't support it.
As to mitigating epidemics, that would require something like a public health system. The antibiotics you can make with primitive technology are very, very basic. They might not help much, or at all, and it is hard to see how people would think to use them against internal diseases at all initially. To make a dent, you will have to distribute a lot of them. Not sure how to do that.