Two basic features were absent at the launch of the Epic Games Store: cloud saving, which is supposed to come soon, and the ability to play games offline. Good news: the latter of the two was quietly added last week.
I can't find a way to manually switch to offline mode, but try this: close the Epic launcher (it doesn't seem to matter if you're signed in or not), disconnect from the internet, and launch it again. It'll let you know that it can't connect, and will give you the option to skip sign-in. Do that, and you should still be able to launch installed games, so long as they don't require a connection to play. I was able to launch Hades and What Remains of Edith Finch.
The feature was introduced last week, but aside from a tweet from director of publishing strategy Sergey Galyonkin—which I obviously missed while I was busy playing New World—I can't find any other announcement. Patch notes would be nice!
I'll set an alert for the next time Galyonkin tweets about cloud saving. Hopefully it comes with the Metro Exodus launch—it would make sense to add the feature with such a big release—but we'll just have to wait and see. In an update last week, Epic said that a roadmap is coming soon.