It can't be done. To understand why you have to know the actual history. Fleming accidentally discovered a contaminating mould killed off his bacterial cultures in Petri dishes.
Did this give the world Penicillin? No, not at all. No-one knew how to produce or culture on any scale.
Come the Second World war and it became imperative to keep wounded soldiers alive. A massive research effort was instigated by Howard Florey and Ernst Chain to find out how to extract and mass manufacture Penicillin. They succeeded and the world now had an extremely effective antibiotic.
Alexander Fleming was given the glory as a discoverer of Penicillin, but he wasn't the first, and a share in the Nobel prize. The real work was done by Florey and Chain.
Earlier civilizations lacked two things to discover and produce Penicillin. One, a knowledge and understanding of bacteria. two, the necessary industrial capacity to manufacture the antibiotic. Basically discovering an antibiotic is only the merest beginning. A brilliant person in an ancient Roman society wouldn't have a chance of doing so. Sorry, about that.
EDIT added 21/11/2019:
The history of Penicillin is complex, long and full of turnings in many different directions. The short story is not find mouldy bread, now make penicillin.
First up, what our forebears knew.
Many ancient cultures, including those in Egypt, Greece, and India, independently discovered the useful properties of fungi and plants in treating infection. These treatments often worked because many organisms, including many species of mold, naturally produce antibiotic substances. However, ancient practitioners could not precisely identify or isolate the active components in these organisms.
Please note: identifying and isolating the active components is the key idea.
The history of penicillin follows a number of observations and discoveries of apparent evidence of antibiotic activity in molds before the modern isolation of the chemical penicillin in 1928. There are anecdotes about ancient societies using molds to treat infections, and in the following centuries many people observed the inhibition of bacterial growth by various molds.1 However, it is unknown if the species involved were Penicillium species or if the antimicrobial substances produced were penicillin.
The early scientific evidence for antibiosis and antisepsis starts with this work.
The modern history of penicillin research begins in earnest in the 1870s, in the United Kingdom. Sir John Scott Burdon-Sanderson, who started out at St. Mary's Hospital (1852–1858) and later worked there as a lecturer (1854–1862), observed that culture fluid covered with mold would produce no bacterial growth. Burdon-Sanderson's discovery prompted Joseph Lister, an English surgeon and the father of modern antisepsis, to discover in 1871 that urine samples contaminated with mold also did not permit the growth of bacteria. Lister also described the antibacterial action on human tissue of a species of mold he called Penicillium glaucum. A nurse at King's College Hospital whose wounds did not respond to any traditional antiseptic was then given another substance that cured her, and Lister's registrar informed her that it was called Penicillium. In 1874, the Welsh physician William Roberts, who later coined the term "enzyme", observed that bacterial contamination is generally absent in laboratory cultures of Penicillium glaucum. John Tyndall followed up on Burdon-Sanderson's work and demonstrated to the Royal Society in 1875 the antibacterial action of the Penicillium fungus. By this time, Bacillus anthracis had been shown to cause anthrax, the first demonstration that a specific bacterium caused a specific disease.
I refer interested persons to this article for more information about early precursor research.
This eventually led to Sir Alexander Fleming's accidental discovery and subsequent research.
In 1928, Scottish biologist Alexander Fleming noticed a halo of inhibition of bacterial growth around a contaminant blue-green mold on a Staphylococcus plate culture. He concluded that the mold was releasing a substance that was inhibiting bacterial growth. He grew a pure culture of the mold and subsequently concentrated what he later named "penicillin". He soon began treating infections in patients with penicillin. One of the first was his assistant Stuart Braddock. Fleming applied penicillin to his Sinus infection. Within three hours, most of the bacteria in the infected area had disappeared. In 1929, he reported his findings in an article for The British Journal of Experimental Pathology. During the next twelve years, Fleming grew and distributed the original mold, which was eventually identified as Penicillium notatum (now known as Penicillium chrysogenum). He was unsuccessful in making a stable form of it for mass production. Although Fleming did some research with penicillin directly on patients and greatly contributed to its medical use, he did not realize its revolutionary potential, due to the impurity of the penicillin he made and the difficulty in mass producing it. Most of his further research with penicillin was focused mostly on the properties of penicillin rather than medical treatment with penicillin.
Please note that Fleming's main problem with his research was in isolating pure enough samples of penicillin. Also, he was investigating its properties, like a good biologist, rather than its medical application.
It was only when the development of techniques for its mass manufacture that the full medical potential of penicillin was realized.
The real problem faced by the OP's person in the past who is endowed with a magical foreknowledge of penicillin is in their ability to isolate sufficiently pure quantities of penicillin. They would also need to be granted magical foreknowledge of microbiology, microbiological laboratory techniques, foreknowledge of the uses and manufacture or production of glassware, and to be magically endowed with the financial and person-power resources to accomplish all this. Knowledge alone of what penicillin is, and what it can do isn't enough.
It took several generations of scientists and research to find useful species of Penicillium and then to develop the techniques for its isolation and purification. It would be wonderful if a, say, Roman who investigating nature, and armed with foreknowledge, could introduce penicillin to the ancient world. The barrier is a legion of practical and technical problems which cannot be whisked away with the notion of oh! that might just work!
To quote Thomas Alva Edison: "Genius is one percent inspiration, and ninety-nine percent perspiration."
The ancient world may have known about applying moulds and poultices to cure wounds, but lacked the technical ability to make penicillin usefully. The amount of perspiration required would fill a large lake.
While I applaud the ingenuity of the OP's concept of penicillin in the ancient world, I cannot believe in it as a practical possibility. YMMV.