Autoplay Video Headers

I’m trying to determine the best way to have a video background header on my website, including a transparent header menu. I started with the “Home – Example 11 (Special)” page for the transparent menu, but need to figure out the best way to have a video play under it. I uploaded a YouTube embed in both the featured image and elsewhere on the page, but it doesn’t autoplay.

There has to be a better way to do this, right? And how do I make the transparent menu work across all of my pages?