Cookie notices should be the first focusable element on the page - put it before navbar/focus links
As a dialog the first focusable element is selected when a user presses enter on it - make this the submit button
You shouldn't animate it in if possible - just have it there. Animating out if fine though (but why bother)
Notice how the action links are display block - this should be copied as inline links dont work the way you want with screen readers.
Use vertical-align/line-height/transform/whatever for text links if you need to