Cross launch or PS5 exclusive my estimate would be the latter since Sony cam sell a lot of PS5 consoles early with a megaton hit as God of War. A new god of war game will at least take 3 full years, this one took 5 years so my estimate would be early or late 2021. The new god of war game is going to be a PS5 exclusive, unless they can somehow easily port it to the PS4.
Please excuse my (probally) poor grammar