Enqueuing a script before anything else

You can change the order of the scripts but can’t have one script load before anything else. The HTML 5 enabling script is IE conditional so you probably don’t want to use wp_enqueue_script as it would load for all browser users which isn’t necessary.

It’s ok to hard code it in your themes header. Even Twentyeleven does it this way.

Also there is nothing that says it has to be added before any styes. It just has to be before the opening <body> tag.