Alright, so, say there are ~55 births per 1000 per year at the time. I'll pretend infant mortality is about 20%, (Roman Egypt's was about 32%, and with breaths and all that, it's probably significantly lower) so about 44 babies per 1000 per year, divide that by about 52 (Number of weeks per year), and you get 0.85 babies per week. If you need ~200 breaths, divide that by 0.85, and you get around 236 thousand people minimum. I'm willing to bet it's at least twice this many, probably closer to three times, as Rome IRL, by conservative estimates, was about half a million, and with the breaths and very fertile soil, its not unreasonable to assume it could support three-quarters of a million.
That's assuming my math is right, and the sources I found are right.