The date of any earlier phonograph will depend on the ability to cut screws repeatedly, accurately, and on an industrial scale. That puts the earliest date, baring any PODs, at 1800 when Maudslay combined all the elements we consider are part of the "modern" screw lathe; slide rest, feed screw, diamond tipped cutters, gear changing, and the rest.
The screw is important due to the need for speed control. In order to accurately play back any recording, you need to revolve the cylinder at or near the same speed it was revolving during the act of recording. You also need to revolve the cylinder at the same speed for the duration of the recording and the playback. Any changes in screw pitch will distort the sounds being recorded and played back as will any changes in screw pitch between machines will have the same effect.
When you are able to repeatedly cut screws, both accurately and in industrial numbers, and there is no reason why the phonograph can't be invented immediately afterward. All of the other components have been around since the Classical Era if not before.
Bill