Simple just build a system like Azure, SONY is not as rich like Microsoft but they can afford if it for making money. Or the easiest one, work with Google, Oracle, or Amazon.
I dont think Sony can afford investing multi billions in a network that will only really benefit there gaming department. PS alone wont turn that figure around any time soon.
MS use Azure for many reasons and actually there gaming Division has little input for it. MS make there money on Azure via other means, something Sony as a corp isnt involved in. Sony is a tech giant not a software giant, a cloud service similar to Azure/Amazon would cost a fortune and wont benefit Sony that much as a whole and PS i dont think will be enough to make back that amount of investments unless they find multiple means for it.
$30b is a huge chunk out of Sony plus its not something i think they can build soon. Will wait and see on there appoach, maybe they will bite the bullet and invest, maybe they will rent the service out, or maybe they wont go the Streaming route. All just assumptions for now.