Fortunately, there's a way to preload maps, but it's not intuitive: type "OK maps" in the search box and tap the search icon. You'll see this message: "pre-loading maps" or an error message: "the on-screen area map is too large, zoom in first". If you see the error message, zoom in and type "OK maps" again. It's annoying to this again and again.
Another downside is that you can't manage your offline maps. Here's a screenshot from the old Google Maps: you could quickly find cached maps, check how much space they use, rename them or delete them.
Hopefully, Google will add the offline feature to the interface in a future update and make it even better. It would be nice to save bigger maps and to use the offline maps for local search, directions and navigation.
Update: A new version of Google Maps added this option when you tap the search box: "Make this map available offline". It's less cumbersome to use, but still a patchwork.