I found the Stooke atlas, which is scarce on info before the space age; and read papers by Wilkins, but I did not find info on when people did recognize that the moon was a tridimensional ball, and this meant there had to be another side.
Any other pre-1953 sources on the farside are well appreciated.
Ancient Greek astronomers believed the moon to be a sphere - here's a relevant post (which ended up largely debating the Earth; you'll have to scroll way down to finally find some discussion on the Moon):
When people thought the Earth was flat, did they think the moon was a 2D circle in the sky?
Kepler, the 17th century German astronomer, wrote a short novel called Somnium (the Dream) describing a journey to the moon and meeting with its inhabitants.
The inhabitants of the dark side of the moon are said to be unfortunate because they do not have the vision of the Earth to contemplate in the sky.
I'm not sure if this is helpful, but a careful observer would be able to see that the moon was not a simple disc. While it presents the same face to the Earth, the moon "rocks" to show different areas around the edges. I'd intended to find a GIF to show this, but APOD is down at the moment.