If you had the tools, something like flasks and petri dishes, you probably COULD culture antibiotic-producing bacteria and fungi,even before 1015. A microscope would be tough, but not strictly needed.
Most antibiotics come from cultured soil bacteria. The culture media could be gelatin, I think, you’d have a hard time getting agar.
Most of the work is in observation and understanding, the tech itself is not terribly tough.
I think one mistake that we’re making is the assumption that we the time traveler would be the only one making the advances.
the people 1000 years ago were no less intelligent than us. They just lived in a more primitive time. If the time traveler were to spend a few years working with Leonardo DaVinci, I think he would succeed with a lot more of his inventions.
I think that if you were to spread your knowledge, others would come up with new ideas on their own. Invention is an evolutionary process. As knowledge spreads, people around the world tend to invent similar things due to necessity. Tesla and Marconi weren’t working together but they were working in the same direction which is how Marconi got credit for the radio till recently.