Computers can do all sorts of marvellous things, without people needing to apply their skills or even be involved at all.
This is why you shouldn't have characters in a game use computers, if you can help it.
Commentary by memnarch (who has not seen the movie)
Alright, seeing the math makes me think a glancing angle is much less plausible than I did before. So of course it's going to work; there wouldn't be a plot device that does just that otherwise. The specific math probably isn't mentioned in the movie, but I suspect this scene likely has a reference to the famous asteroid field in Episode V in it. Including Han complaining about commentary on his flying abilities.
Chewie also raises an excellent point. Why does a nav computer, which I think I remember Han telling Luke about in Episode IV to shut him up, exist in the Millennium Falcon, when the movies do show Han as manually pulling a lever or handle? The Doylist reason is that it'd be odd to not show the characters doing something to make it happen. With how prolific Star Wars fiction was before the sequel movies, there's probably a Watsonian reason as well but dang if I know what it could be.
Chewbacca: I’ve done some calculations. If the shield is 100 kilometres from the surface, we’ll cover that distance in a third of a millisecond.
Zeppo: We’ll come in at a glancing angle!
Chewbacca: What's the Moon’s diameter?
GM: Er... 4900 kilometres.
Chewbacca: Optimistically, that gives us up to... 1400 kilometres inside the shield without smashing into the Moon. That’s a 4.6 millisecond window to exit lightspeed. More or less.
Zeppo: We’ll just set the nav comp to calculate where we are and exit hyperspace at the right moment.
Chewbacca: You do realise that every other time we’ve entered or exited hyperspace, it’s been by throwing a lever.
Finn: The computer can’t do it for us?
Zeppo: You’ll just have to do your best, Chewie.
Chewbacca: And if I fail?
Zeppo: Everyone will say at least you tried.
Chewbacca: To hit the lever at the right instant?
Zeppo: To talk me out of it!