Follow up on an old question/idea.
My 'time traveler' (actually more of a dimension hopper) got thrown into a roughly medieval feudal society, very closely modeled off of, but not the same as, medieval Europe without warning.
He earns the interest of the kings youngest son, a prince that is mostly written off as too much of a scholar without enough leadership material and clearly not the king's favorite. The son argues that our protagonists future knowledge can be valuable, but the king is highly skeptical and considers him a charlatan, willing to humor him with a place to stay for his son's sake but not to seriously consider any of our protagonists suggestions.
The protagonist likewise has a hard time getting traction for improvements from others due to the difficulty in proving his theories and the king's skepticism rubbing off on his retainers. That is until he recommends boiling water as a (sadly only viable to the nobility...) protection against a Cholera like disease.
Our protagonist then suggests he'd like to use the kings newfound willingness to listen to him to try to rediscover penicillin. The only problem is that he doesn't have a good method for doing that.
However per Nosajimiki answer on the first link above penicillin should already be known by cheese makers and possible doctor who use it to treat wounds. Unfortunately our protagonist doesn't know that these folks are aware of penicillin and has no reason to think of asking a cheese maker to help him with revolutionizing medicine. Thus the question is rather our time traveler can stumble upon the fact that penicillin already exists and doesn't need to be recreated from scratch.
The most obvious avenue for this would be a doctor mentioning they use mold to treat wounds when he says he's looking for a mold that will stop disease. This is made a little harder because many doctors are already weary of him, they don't like his trying to revolutionize so much of their knowledge and really hate to be told they may be spreading disease with their practices. Thus he's getting rather lackluster assistance from the medical professionals available to him.
So how likely is it that when he shows up and tells the king there is a mold that is a miracle medicine and he just needs to find it someone will tell him he's an idiot it already exists? will they recognize his, very limited, description of the mold?
If they do how hard would it be to take existing penicillin and make it into an ingestible antibiotic? Can people just eat the mold cheese makers already have and bam your done (...assuming they had a sickness penicillin can treat of course)? How hard would it be to prove that the mold the cheese maker has is penicillin if he doesn't know which diseases it treats and he just tries to have everyone take it. Yes I'm aware of the risk of encouraging evolution of penicillin immune diseases, but I suspect penicillin won't be used reliable enough for that to be a big risk yet and doesn't really need to be in focus for this story.
Not sure how much my world specific matter, beyond being Europe-like. But our protagonist does not have a medical degree, thus he doesn't know lots of things such as what penicillin should look like. He is however smart with a fairly wide breadth of knowledge and a love and in depth understanding of evolution, though he is afraid to teach that for fear of angering the powerful church that is already slightly weary of him. This evolution knowledge leads to a decent understanding of germ theory and how diseases spread, but from the perspective of how they are evolving not from how modern doctors combat them. He knows lots of generalities about how doctors in the past addressed things, but not enough of the specifics to be certain he can recreate the steps they used.