in the gltf export dialog make sure your format(in the drop down) is set to "embedded" and not binary or separate files...I have not checked in a while but not only is embedded faster it has also been more reliable.
try this:
export you object to your desktop(you can't miss that right :) )
then locate where your project folder is. You can do that by...
1) opening Godot(do not open your project)
2) at the bottom right of the project icon there is a little file tree image and beside that is the directory....
simply click on the little file tree image.
-that will open up the correct folder
3) move the file from your desktop into that folder....
That should be it, when you open your project it should be listed there....if it is...follow these steps.
1) double click the object - you will presented with a dialogue. Simply click "open anyway"
2) save that scene somewhere inside your game directory with a name that reflects the model or level...they share the same file extension.
3) let me know how it goes. :)