The game definitely isn’t ready for underground cities yet. So far, they more or less have tunnel digging ready for mining. The current bunch of hearthlings are really above ground dwellers at heart, so they are more worried about houses than caverns.
Having said that, there will eventually be an actual dwarf civilization you can play as, so we can expect better support for cave living eventually.
Digging up is definitely difficult in the current game (and not really supported properly yet), but it’s possible. Check out this topic.