So if you've used Premiere Pro then this will make sense, but basically I have a very long document and when I remove an object from the middle, I have to select everything underneath and nudge it up. I was wondering if there's an easier way to make everything move up to fill the empty space that I deleted from.
No there is no such thing. There really can not be such a thing without inventing something to represent nothing, other than empty. But if you can identify anddescribe what that nothing is then I'm sure such a tool could be built.
See empty space is as valid design as nonempty space. Maybe your looking to compress/auto layout artboards, but why not use InDesign then?
"Very long document" and "Adobe Illustrator" don't really go together. As @joojaa mentioned, you very well may be better off using InDesign for a document of any length. Artboards in Illustrator are there to allow you to have separate canvases to work on, but shouldn't be used as "pages" of a long document. InDesign is a much better tool.
If you needed a hole in a piece of wood, you could technically use a hammer and nail to do the job, but you'd have a much easier time (and many better options) by using a drill.
All that said, to answer your main question... No, there isn't a good way in Illustrator to do what you're asking (but there is in InDesign!).