Uncontrolled lighter-than-air flight is so easy to see in nature (ashes rising in a fire) or create on a small scale by simply holding a paper sack over a fire that it is amazing that tethered or free hot-air balloons were not invented by a whole host of ancient civilizations. Perhaps the principle was known but no one really saw any value to it.
Regardless of how early free balloons are invented, it is hard to imagine efficient dirigibles much predating the 20th century, when light alloys and small internal combustion engines are invented. There may be other types of propulsion (human-powered propellors, or steam) which might be possible earlier, but it would take a very different evolution of technology than occurred in our world, where it took over 100 years of fanciful and unsuccessful dreaming of wind, oar, and animal powered airships before the first true dirigibles were possible.