I tried downloading the content examples from the launcher and it kept getting stuck at 600 MB, I deleted the local content but that didn’t fix it.
I am running the launcher with administrator rights and there is enough space left in my storage.
Video of the issue:
I had this problem as well in the past.
The only way I could fix it was using an internet speed of 600kb/s for it to work.
Maybe trying “-http=winnet” might work for you?
I would use an Internet speed of 600 kb/s but I only get 240 kb/s, so that isn’t possible.
What is “-http=winnet”?
Yeah… I had to go to a library to do that.
“-http=winnnet” is something you add to the end of the path in the exe. (Or shortcut) Just add that and see if it helps. (Without the quotes in it. :D)
What does it do?
It changes the way it uses the internet? Or how it connects?
I really don’t know off the bat what it really does, But it did help me in downloading things.
And it helped my friend who had a similar problem.
Try it and see if it works! No harm done to anything from it! 
Found this link here while typing! Epic Game launcher stuck at download - Getting Started & Setup - Epic Developer Community Forums Maybe this will help?
If not contact Epic’s support for launcher via Email.