Use a browser developer tool for these kinds of CSS exploratory queries.
I used Google Chrome's built-in developer tool and discovered the parent
<div> of your header has a background colour [screenshot].
This means you either have to remove the background colour on this parenting div and re-apply it to all other elements that you still want it to affect. Or you'll have to move your header out of its parent div, so it is no longer contained and constrained by the white background colour style.
The first solution may require a lot of CSS changes; applying the white background to a lot of HTML elements.
The second solution will require a Child Theme. You'll have to copy the theme's header.php file into your Child Theme directory and then modify that.
Remember, you should never edit the theme's files because you'll only (well, that's one reason) lose your changes when the theme updates. To avoid this, use a Custom CSS Manager plugin (for CSS-only changes) or a Child Theme (for CSS and all other changes).