We know that the Romans invented or used simple machinery like waterwheels, crank mechanisms and even simple steam and atmospheric engines, as well as what we would recognize today as clockwork, but for a variety of reasons, the Romans never got beyond individual pieces of bespoke machinery for particular applications, and certainly never triggered an industrial revolution in the first century AD, or any time.
What I would like to know is, assuming no large scale discontinuities like civil wars or the fall of the Empire, would it be possible for the Romans to have built a simple flying machine at any time, and what circumstances would possibly allow this?
Edit to add: For clarification, could the Romans have developed a heavier than air flying machine either with the technology available after the first century AD or evolved form beyond that point?