The finite speed of light was discovered in the late 17th century by Ole Romer from the timing of eclipses of Jupiter's moons -
https://en.wikipedia.org/wiki/Rømer's_determination_of_the_speed_of_light Remarkably, he was within 30% of the modern value. It took a while to be accepted, but by Talbot's time this was established scientific fact that I expect he was aware of.
However, the size of the universe, or galaxy, was much less well known. Through measurements of parallax (or lack of observable parallax) and of binary stars, the Herschels (William, Caroline, John) understood that the stars are very far away, and William published the idea of the Galaxy as a flattened disk of stars in 1785:
https://en.wikipedia.org/wiki/William_Herschel#/media/File:Herschel-galaxy.jpg
In the 18-19thC, as others have said, the Galaxy was thought to be the extent of the universe, other nebulae were not yet understood to be separate galaxies. I don't know offhand what the Herschels thought the extent of the Galaxy was, but guessing they knew it was at least hundreds of light years across. (It's actually a few ten thousands and we are ~8 kiloparsecs from the center, about 25000 light years.) Measurements of the extent and size of the Milky Way were systematically incorrect until the discovery of interstellar absorption by Trumpler in the early 20thC. I am not aware of who first wrote about the philosophical implications of the finite speed of light on seeing stars as they were in the past.