The declination pattern for the case endings, as well as the article ὁ, ἡ, τό, seems to fairly closely match that of the grammatical endings you find in Latin:
The -us/-ος similarity is plain to see (and makes perfect sense considering how Old Latin /-os/ was raised to /-us/); the same pattern happened with Old Latin /-om/ > /-um/, and the interchangability of /m/ and /n/ we see in several other languages, such as German -n for accusative, but English or Norwegian -m for the same (him/ham for instance) is a common pattern in Germanic and Latin languages, as far as I know. Thus we have a place for the accusative -um/-ον|-am/-αν/-ην relationship. The relationship between -ō and -ου/-ῳ are again plain enough to see, as well as -ae/-ᾱͅ/-ῃ (considering the overlapping of the dative and ablative in Latin with the genitive and dative in Greek). The odd one out, it seems, is the -ᾱς/-ης in genitive feminine singularis.
Viewing the etymology of the Greek article on Wiktionary, we are informed that it stems from PIE *só, *séh₂, *tód, almost exactly matching ὁ, ἡ, τό; I would assume the initial s- was muted fairly early on, and the same for the final -d.
I have by way of Latin and German come to expect /-m|-n/ and /-s/ to be signs of an accusative (and verily the /-s/ is exactly what you find in the plural both in Latin and in Greek (though not in German). How did that pesky /s/ end up sneaking its way into the Greek genitive feminine singularis, and not in masculine/neuter?