I know it’s been the predominant assumption throughout human history but the idea of believing Earth is the only harbinger of life in existence, is something I find hard to imagine. I've believed in alien life as long as I can remember, I’ve believed in the likely existence of parallel universe Earths almost as long.
That is a great question, I do not know if there are any philosophical arguments for this, but you may or may not have heard of True History, or True Fictions by Lucian of Samosata, it was intended as a work of parody, satirizing the trend of many Greek historians and authors of regarding mythological and fictitious events as being true. But the interesting bit is the plot itself: It follows a group of heroes who set out from the Pillars of Hercules and during their journey end up being sucked up by a whirlwind which carries them to the Moon where they find themselves in the middle of a war between the Sun and the Moon to colonize the Morning Star.
The Sun, the Moon, Morning Star and other celestial bodies are all described as being unique locales with their own geographies and species (centaurs, purple-coloured plants, a race without females where the infants are born out of the calves of the men etc.).
This was inspired by Diogenes who wrote a book called Of The Wonderful Things Beyond Thule, where the hero also journeys to the Moon, so the idea was not original, and it is difficult to tell if there were even earlier stories with similar plots.
Greek and by extension Roman legends often contain far-off exotic lands containing fantastic beasts and strange peoples as everything beyond the edges of the map was in large part unknowable but at the same time they realized that the works of Homer and Herodotus were to be taken as allegories. Usually these places were uncharted islands or even relatively unknown lands like India or Egypt that being on the edge of the collective consciousness were rumored to contain strange creatures and hidden magic, but in some plays and stories other worlds are mentioned.
Later on around 800-1000 the collection of tales One Thousand and One Nights describes travelling across the cosmos to visit otherworlds and meet their inhabitants, particularly in "The Adventures of Bulukiya", but in several other stories as well.
Can I make the wild guess that this question was prompted by Neal Stephenson's Anathem? If not, go read it. It's fiction, but it ties together those two things (classical philosophy and alien life) quite neatly.