When I press H then Esc to enter and exit the inventory menu, most of my UI disappears. This includes the in-game UI like meters and equipped items, interact prompts, and the middle mouse button crafting menu, but not things like tutorial pop-ups and npc inventories. It removes the word "climb" and the E key icon from the climb prompts, but not the lil pyramid indicator.

(It also doesn't get rid of a couple of weird debug UI things that remain in the game for some reason: the fps/level info overlay that pressing O brings up or the odd "test [random letter]" text that pressing N creates.)

Doing this early in the tutorial area on the boat leads to needing to force quit the game at the lockpick crafting tutorial, since the crafting interface is invisible and as far as I can tell you cannot leave this screen except by crafting lockpicks, and that's pretty difficult to do with an invisible UI. At this point it seems that you have to start over completely, with no progress during the tutorial being saved, and that there's no way to skip through dialogue once you're going through the tutorial again.

When the UI disappeared while I was playing the first mission this rendered the game extremely difficult to play, so I quit and reloaded. This put me back in bed, with the objective to select a job for the night (instead of the objective you usually have the first time you wake up), and kept any items I had in my inventory during the mission. When I entered Pickman's bar, he wasn't there and I didn't get the conversation I had with him the first time. Interacting with the mission board shows no available missions, and trying to leave tells me that I need to pick a mission. At this point there seems to be no way to proceed and you just have to play through the entire, unskippable tutorial yet again.

I don't know what happens if you quit during other missions or later sections of the game, since I have been unable to get that far.

Interacting with the mannequin you use to change outfits in Pickman's bar brings the UI back, but this obviously doesn't help when I seem to be unable to proceed in the game because no missions are available.

I also experienced an infinite loading screen at one point while testing all this, but unfortunately I don't know what was different about that time that could have caused the problem, and I received the "Pro-Ghosting" achievement immediately upon launching the game for the first time.