D. N. Brooks, in Hearing aids – a historical survey states that Emperor Hadrian
reportedly used to cup his hand behind his ear, the better to hear the affairs of state...Historically, the cupped hand was probably first replaced by a rolled up leaf or hollowed out animal horn.
There are references to medieval hearing aids in a number of articles online. For example, The (Big) Timeline of Hearing Aids states (under the heading 13th to 15th century):
Really early on, people would use animal horns and hallow bones as sort of an ear trumpet. While it helped a small amount, it was nothing close to an ear trumpet made of metal. It was the first sign of an attempt to aid the hard of hearing.
Also, the Textbook of Hearing Amplification, with reference to K. Berger’s The Hearing Aid, says that animal horns were used to aid hearing as early as the thirteenth century.
wood carvings that resemble animal ears used to help people hear
Despite these references, the only images I have found from before the 17th century appear to be false leads: this picture taken in the Musee d'histoire de la medecine in Paris appears to have been mislabelled as medieval, likewise this picture. This Wikipedia article is of little help; it dates hearing aids as late as the 17th century (see example below).
Early Modern period (1673) "Ear trumpets, as illustrated in: Athanasius Kircher's Phonurgia nova sive conjugium mechanico-physicum artis & naturae paranymta phonosophia concinnatum. Kempten : Rudolph Dreherr, 1673. (p. 160)."
Even in Ancient times, it is possible that some kind of hearing aid may have been used. Given that the Ancient Greeks had an in-depth understanding of voice amplification and acoustics (see this pdf), it is not inconceivable (but I’m not assuming) that they had an aid for hearing loss, just as they did for poor eyesight (see this Hist SE link). However, the only references I’ve found relate to people born deaf (and they aren’t very complimentary): there appears to be nothing online relating to hearing loss in the ancient world.
In short, the references I've found are at best vague and do not give any details or show any evidence or cite any contemporary sources. At worst, the information appears to be wrong. However, there is enough here to suggest that there may be evidence from the medieval period, if not earlier.
Aside from the use of the hand to cup the ear, what is the earliest evidence for the use of some kind hearing aid? Evidence (which can be dated at least approximately) could be:
an archaeological find
a reference to some kind of hearing aid in a contemporary source
a contemporary image of some kind (painting, engraving etc)