There is no special setting that would help you to resolve this issue but there is a workaround, that behaves as expected. For this follow the steps
Add a New or Existing Web Site to the Solution.
Just make sure it's created inside your solution folder.
even create a "link" to an external folder, e.g. 'Docs' on a network share. In that case, it's ignored by Git of course.
Make sure to go to the "Project" settings or Configuration Manager to exclude this "Web Site" from Build and Deploy.
Done. Now Solution Explorer will reflect any change in the file system and vice versa.
This is not the official feature though but it helps you to have the solution folders as real folders.