Like I get that the Norse games are the ones praised specifically for their story, but I'm not even sure why you would want to skip the Greek ones.
All the violence, sex and dark themes? - Obviously not given how much of a hit Game of Thrones was and how they've basically tried to turn every gritty fantasy series released afterwards into GOT ever since. Not to mention that, while definitely not AS DARK as the Greek games, the Norse games' story isn't exactly sunshine and rainbows.
How unlikable Kratos is in those games? - Well first off, we need to see him being a monster first for his eventual redemption to have the impact you want it to. Second, if you're going chronologically then you have FOUR straight games worth of material (Ascension, Chains of Olympus, GOW1 and Ghost of Sparta), all of which feature a Kratos who (while deeply flawed) is sympathetic enough that you can still root for him. It's only really GOW 2 and 3 that he stops giving any kind of a shit and goes full asshole (and even then, GOW3 still had Pandora) which IF you adapt it right should be a perfectly believable transition given all the shit he's been through.
Lack of strong female characters maybe? - Athena is a prominent character in every single Greek God of War game, not to mention the abundance of other powerful Goddesses you could feature which either never appeared in the games or we don't know what happened to them (
coughArtemiscough). You could do something with that. Hell he goes to the Underworld in several games and there is currently a game set to be released featuring a daughter of Hades who hasn't been in very much. Just a thought.
The Game's stories are too short? - Perfect for making short seasons out of them. Not to mention, if you NEED to extend the length of them, there are a metric fuck-ton of Greek monsters and gods who never featured in the series at all which you could use for filler.
If anything the Greek games would seem to me to be an easier sell for a TV series, I really don't get why they would skip them, seems like you're passing up a gold mine there.